1rBTX 01. NOMBRES REALS/1.1.3 Ordre, arrels i operacions 1.1.3.000DT DEFINICIÓ ARREL NÈSIMA Arrel n-èsima

S'anomena arrel n-èsima del nombre x, el nombre y que elevat a n dona x: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«/math»

També es pot escriure com un exponent FRACCIONARI:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»m«/mi»«/msup»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mfrac»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mfrac»«/msup»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.00DT ORDRE EN ELS REALS

Ordre en els nombres reals

En els nombres reals, la relació "≤" o "≥" és una relació d'ordre (reflexiva, simètrica i transitiva).

Es pot definir amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8804;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8804;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.01 Ordenar reals Ordena, de petit a gran, els nombres reals següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«/mrow»«/mstyle»«/math»

Format: {1,2,3,4,5}

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a13</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a14</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a15</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msqrt><mi>a11</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfrac><msqrt><mrow><mi>a11</mi><mo>+</mo><mi>a12</mi></mrow></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mfrac><mrow><msqrt><mi>a12</mi></msqrt><mo>-</mo><msqrt><mi>a13</mi></msqrt></mrow><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mfrac><msqrt><mi>a13</mi></msqrt><msqrt><mi>a14</mi></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mfrac><mrow><msqrt><mi>a11</mi></msqrt><mo>+</mo><mi>a15</mi></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>ordena</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>,</mo><mi>a4</mi><mo>,</mo><mi>a5</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>,</mo><mi>a4</mi><mo>,</mo><mi>a5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>11</mn></msqrt><mo>,</mo><mfrac><msqrt><mn>23</mn></msqrt><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>11</mn></msqrt><mn>2</mn></mfrac><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>23</mn></msqrt><mn>2</mn></mfrac><mo>,</mo><msqrt><mn>11</mn></msqrt><mo>,</mo><mfrac><msqrt><mn>11</mn></msqrt><mn>2</mn></mfrac><mo>+</mo><mn>9</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> N'hi ha prou amb aproximar els nombres amb la calculadora per ordenar-los.

]]> 1.1.3.11Q AgrupaRadicalsSemblants Agrupa els radicals semblants en l'expressió (no confonguis els símbols de restar - i de multiplicar ·):
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>i_1</mi><mo>≠</mo><mi>i_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>c_1</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>c_2</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>c_3</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>c_4</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a_1</mi><mo>-</mo><mi>a_2</mi><mo>+</mo><mi>a_3</mi><mo>-</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>c_1</mi><mo>+</mo><mi>c_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mo>-</mo><mi>c_2</mi><mo>-</mo><mi>c_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><msqrt><mi>i_2</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>20</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Es tracta de sumar o restar els coeficients dels termes que tenen el mateix radical:

Per #e_1, el coeficient és: #d_1 = #c_1 + #c_3

Per #e_2, el coeficient és: #d_2 = -#c_2 - #c_4

]]> 1.1.3.12Q Agrupar radicals semblants_2 Agrupa els radicals semblants en l'expressió:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>i_1</mi><mo>≠</mo><mi>i_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>c_1</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>c_2</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>c_3</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>c_4</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>a_2</mi><mo>-</mo><mi>a_3</mi><mo>-</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>c_1</mi><mo>-</mo><mi>c_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mi>c_2</mi><mo>-</mo><mi>c_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><msqrt><mi>i_2</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>4</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Es tracta de sumar o restar els coeficients dels termes que tenen el mateix radical:

Per #e_1, el coeficient és: #d_1 = #c_1 - #c_3

Per #e_2, el coeficient és: #d_2 = #c_2 - #c_4

]]> 1.1.3.21Q SimplificaArrelQuadrada Simplifica: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn»3«/mn»«mroot»«mn»6«/mn»«mn»4«/mn»«/mroot»«/mrow»«/mstyle»«/math»

]]> 1.1.3.22Q SimplificaArrelQuadrada Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msqrt»«/mstyle»«/math»

Format de resposta: semblant a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mroot»«mn»6«/mn»«mn»4«/mn»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><msup><mn>2</mn><mi>a</mi></msup><mo>*</mo><msup><mn>3</mn><mi>b</mi></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mn>100</mn><mo><</mo><mi>e1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>e1</mi><mo><</mo><mn>1000</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msqrt><mi>e1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>216</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>6</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La descomposició en factors del radicand és 2^#a · 3^#b
¨Surt/en¨ #n dos/os i #n tresos i queda un dos sota l'arrel perquè:

dividim #a per 2 i ens dona #q1 de quocient i #r1 de residu.
dividim #b per 2 i ens dona #q2 de quocient i #r2 de residu.

]]> 1.1.3.25Q SimplificarArrelCúbica Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mroot»«mn mathvariant=¨bold¨»6«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><msup><mn>2</mn><mi>a</mi></msup><mo>·</mo><msup><mn>3</mn><mi>b</mi></msup><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mroot><mi>r_2</mi><mn>3</mn></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mroot><mn>30</mn><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La descomposició en factors del radicand és 2^#a · 3^#b · #c

]]> 1.1.3.26Q SimplificaArrelCúbica Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mstyle»«/math»

Format: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mroot»«mn»6«/mn»«mn»4«/mn»«/mroot»«/math»

]]> 1.1.3.28Q SimplificarFinsIrreductible Simplifica al màxim l'arrel: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mroot»«/mstyle»«/math»

]]> 1.0000000 1.0000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>i1</mi><mo>,</mo><mi>e1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mfenced><mrow><mi>i1</mi><mo>></mo><mi>e1</mi></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i2</mi><mo>=</mo><mi>w1</mi><mo>*</mo><mi>i1</mi></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>w1</mi><mo>*</mo><mi>e1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>e2</mi><mo><</mo><mn>8</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e1</mi></msup><mi>i1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msup><mi>a1</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msup><mi>a1</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e2</mi></msup><mi>i2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>r1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>9</mn></mroot><mo>,</mo><mroot><mn>2</mn><mn>9</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>,</mo><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>,</mo><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>9</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«msup mathcolor=¨#000066¨»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mstyle»«/math»

cal simplificar la fracció: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.1.3.31Q IntroduirFactorsArQuadrada Introdueix tots els factors sota el radical: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><mi>z</mi></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><mi>y</mi><mo>*</mo><msqrt><mrow><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><mi>z</mi></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msup><mi>x</mi><mn>6</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>*</mo><mi>z</mi></mrow></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quan un factor entra sota l'arrel:
a) el seu exponent queda multiplicat per 2
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.32Q IntroduirFactorsArQuadrada_2 Introdueix tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]>

]]> 1.0000000 0.5000000 0 0 #r <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msup><mi>x</mi><mn>5</mn></msup><mo>*</mo><mi>y</mi><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup><mo>*</mo><msqrt><mrow><msup><mi>x</mi><mn>5</mn></msup><mo>*</mo><mi>y</mi><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msup><mi>x</mi><mn>7</mn></msup><mo>*</mo><msup><mi>y</mi><mn>7</mn></msup><mo>*</mo><msup><mi>z</mi><mn>13</mn></msup></mrow></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quan un factor entra sota l'arrel quadrada:
a) el seu exponent queda multiplicat per 2
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.33Q IntroduirFactorsArQuadrada Introdueix tots els factors sota el radical: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»y«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»z«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«/msqrt»«/mrow»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #r <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>d</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>e</mi></mrow></msup><mo>*</mo><msup><mi>z</mi><mrow><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>f</mi></mrow></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msup><mi>x</mi><mn>9</mn></msup><mo>*</mo><msup><mi>y</mi><mn>10</mn></msup><mo>*</mo><msup><mi>z</mi><mn>11</mn></msup></mrow></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quan un factor entra sota l'arrel quadrada:
a) el seu exponent queda multiplicat per 2
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.35Q IntroduirFactorsArrCúbica Introdueix tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow><mn>3</mn></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow><mn>3</mn></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi><mo>*</mo><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><msup><mi>x</mi><mn>13</mn></msup><mo>*</mo><msup><mi>y</mi><mn>10</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup></mrow><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Quan un factor entra sota l'arrel cúbica:
a) el seu exponent queda multiplicat per 3
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.36Q IntroduirFactorsArrCúbica_2 Introdueix tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow><mn>3</mn></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow><mn>3</mn></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi><mo>*</mo><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><msup><mi>x</mi><mn>13</mn></msup><mo>*</mo><msup><mi>y</mi><mn>10</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup></mrow><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Quan un factor entra sota l'arrel cúbica:
a) el seu exponent queda multiplicat per 3
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.40DT OPERACIONS AMB ARRELS Producte d'arrels El producte de dues arrels de mateix índex és igual a l'arrel del producte dels radicands. Quocient d'arrels

El quocient de dues arrels de mateix índex és igual a l'arrel del quocient dels radicands

Potència d'una arrel

La potència d'una arrel és igual a l'arrel de lapotència del radicand.

Arrel d'una arrel

Per calcular l'arrel d'una arrel, n'hi ha prou amb multiplicar els índex.

]]> 0.0000000 0.0000000 0 1.1.3.41Q ProducteArrelsQuad Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«/mrow»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>9</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>9</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msqrt><mrow><mn>6</mn><mo>*</mo><mi>a_1</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msqrt><mrow><mn>10</mn><mo>*</mo><mi>b_1</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mn>6</mn><mo>*</mo><mi>a_1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>b_1</mi></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a_1</mi><mo>≠</mo><mi>b_1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>6</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>15</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msqrt><mn>10</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal multiplicar els radicands entre ells i simplificar si s'escau.

]]> 1.1.3.42Q ProducteArrelsQuad_2 Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #r_22 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msqrt><mrow><mi>d</mi><mo>*</mo><mi>a_1</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msqrt><mrow><mi>d</mi><mo>*</mo><mi>b_1</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_22</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>15</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>21</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msqrt><mn>35</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_22</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> Cal multiplicar els radicands entre ells i simplificar si s'escau.

]]> 1.1.3.43Q QuocientArrelsQuadrades Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«/mfrac»«/mstyle»«/math»

Format de la resposta: enter o «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>19</mn><mo>,</mo><mn>23</mn><mo>,</mo><mn>29</mn><mo>,</mo><mn>31</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>19</mn><mo>,</mo><mn>23</mn><mo>,</mo><mn>29</mn><mo>,</mo><mn>31</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msqrt><mrow><mn>8</mn><mo>*</mo><mi>a_1</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msqrt><mrow><mn>12</mn><mo>*</mo><mi>b_1</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mn>8</mn><mo>*</mo><mi>a_1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mn>12</mn><mo>*</mo><mi>b_1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a_1</mi><mo>≠</mo><mi>b_1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msqrt><mfrac><mrow><mn>8</mn><mo>*</mo><mi>a_1</mi></mrow><mrow><mn>12</mn><mo>*</mo><mi>b_1</mi></mrow></mfrac></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>a_1</mi></mrow><mrow><mn>3</mn><mo>*</mo><mi>b_1</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>numerador</mi><mo>(</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>denominador</mi><mo>(</mo><mi>f1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>88</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>156</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>22</mn><mn>39</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn><mo>,</mo><mn>39</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>858</mn></msqrt><mn>39</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal dividir els radicands entre ells i simplificar i/o racionalitzar si s'escau.

]]> 1.1.3.44Q QuocientArrelsCúbiques Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

Format de la resposta: enter o «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>18</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>18</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mroot><mrow><mn>2</mn><mo>·</mo><mi>a_1</mi></mrow><mn>3</mn></mroot></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mroot><mrow><mn>2</mn><mo>·</mo><mi>b_1</mi></mrow><mn>3</mn></mroot></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mroot><mfrac><mi>a_1</mi><mi>b_1</mi></mfrac><mn>3</mn></mroot></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a_1</mi><mo>></mo><mi>b_1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b_1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>36</mn><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>20</mn><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mroot><mn>225</mn><mn>3</mn></mroot><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És el mateix que: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#0000FF¨»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mstyle»«/math»

Cal simplificar si s'escau.

]]> 1.1.3.45 Arrel d'una arrel Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mroot»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #r_22]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><msup><mfenced><mrow><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>19</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>r_22</mi><mo>=</mo><mroot><mi>a</mi><mi>i</mi></mroot></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>m</mi><mo>≠</mo><mi>n</mi></mrow></mfenced></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>256</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>7</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>22</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal multiplicar els índex entre ells i simplificar si s'escau.

]]> 1.1.3.50DT REDUCCIÓ A ÍNDEX COMÚ Reducció a índex comú

Per reduir a índex comú, es fa com en les fraccions:

es calcula el mcm dels índex
s'escriuen fraccions equivalents amb aquest mcm de denominador. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»mcm«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»18«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8594;«/mo»«mroot mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»18«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mroot mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»9«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»7«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mn mathvariant=¨bold¨»18«/mn»«/mroot»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.51Q CalcularMínimComúÍndex Quin és el mínim comú índex dels radicals següents?

#b_1, #b_2, #b_3

]]> 1.0000000 0.5000000 0 0 #r_13 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a_1</mi><mo>≠</mo><mi>a_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mroot><mn>2</mn><mi>a_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mroot><mn>2</mn><mi>a_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><msqrt><mn>2</mn></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>r_13</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>15</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>210</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_13 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> És el mínim comú múltiple de 2, #a_1 i #a_2
Cal fer la descomposició en factors i agafar un factor de cada, amb els exponents més grans: #d

]]> 1.1.3.52 Calcular mínim comú índex_2 Quin és el mínim comú índex dels radicals següents?

#b_1, #b_2, #b_3

]]>

]]> 1.0000000 0.5000000 0 0 #r_13 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a_1</mi><mo>≠</mo><mi>a_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mroot><mn>2</mn><mi>a_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mroot><mn>2</mn><mi>a_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><msqrt><mn>2</mn></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>r_13</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>15</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>210</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_13 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> És el mínim comú múltiple de 2, #a_1 i #a_2
Cal fer la descomposició en factors i agafar un factor de cada, amb els exponents més grans: #d

]]> 1.1.3.53 Calcular radical equivalent Quin és el valor de m que fa certa la igualtat: #a_1 = #a_2?

Format de la resposta: m=4

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>b</mi></msup><mi>i_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>i_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>m</mi></msup><mi>i_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>a_1</mi><mo>=</mo><mi>a_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>b</mi><mi>i_1</mi></mfrac><mo>=</mo><mfrac><mi>m</mi><mi>i_2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>625</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mn>5</mn><mi>m</mi></msup><mn>35</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>m</mi><mo>=</mo><mn>20.</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>20.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Si els dos radicals són equivalents, cal que les fraccions que representen els seus exponents siguin equivalents. S'ha de resoldre l'equació: #t.

]]> 1.1.3.54 Calcular radical equivalent_2 Quin és el valor de m que fa certa la igualtat: #a_1 = #a_2?

Format de la resposta: m=4

]]>

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>b</mi></msup><mi>i_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>i_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>m</mi></msup><mi>i_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>a_1</mi><mo>=</mo><mi>a_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>b</mi><mi>i_1</mi></mfrac><mo>=</mo><mfrac><mi>m</mi><mi>i_2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>625</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mn>5</mn><mi>m</mi></msup><mn>35</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>m</mi><mo>=</mo><mn>20.</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>20.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Si els dos radicals són equivalents, cal que les fraccions que representen els seus exponents siguin equivalents. S'ha de resoldre l'equació: #t.

]]> 1.1.3.61Q Reduïr Mcíndex Multiplicar Redueix a mínim comú índex i multiplica: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

Format de la resposta: arrel simplificada

Després eleva els radicands #a_1 i #a_2 per tal que els radicals siguin equivalents.

]]> 1.1.3.62Q ReduïrMcíndexMultiplica_2 Redueix a mínim comú índex i multiplica:

Format de la resposta: arrel simplificada

]]> 1.0000000 0.5000000 0 0 #r <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mroot><msup><mfenced><mi>a_1</mi></mfenced><mi>b_1</mi></msup><mi>i</mi></mroot></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mroot><msup><mfenced><mi>a_1</mi></mfenced><mi>b_2</mi></msup><mi>j</mi></mroot></mtd></mtr></mtable><mrow><mfenced><mrow><mi>i</mi><mo>≠</mo><mi>j</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>b_1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>j</mi><mo>,</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>r1</mi><mo>*</mo><mi>r2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mroot><mn>4</mn><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>32</mn><mn>9</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mroot><mn>4</mn><mn>9</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer calcula el m.c.m de #i i #j.

Després eleva els radicands #a_1 i #a_2 per tal que els radicals amb el mcm com a índex siguin equivalents als de l'enunciat; per exemple cal transformar «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»en«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mroot mathcolor=¨#0000FF¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»5«/mn»«/msup»«mn mathvariant=¨bold¨»15«/mn»«/mroot»«/mstyle»«/math»

]]> 1.1.3.63Q ReduïrMcíndexMultiplicar_3 Redueix a mínim comú índex i multiplica: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«/mstyle»«/math»

Format de la resposta: arrel simplificada

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>6</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mroot><mi>a1</mi><mi>i</mi></mroot></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mroot><mi>a2</mi><mi>j</mi></mroot></mtd></mtr></mtable><mrow><mfenced><mrow><mi>i</mi><mo>≠</mo><mi>j</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcm</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>≠</mo><mi>i</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcm</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>≠</mo><mi>j</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>a2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>r1</mi><mo>*</mo><mi>r2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>m</mi><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mi>m</mi><mi>j</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msup><mi>a1</mi><mi>m1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msup><mi>a2</mi><mi>m2</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>4</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>6</mn><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>m1</mi><mo>,</mo><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>10368</mn><mn>12</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer calculo el m.c.m dels índex #i i #j que és #m. Aquest és l'índex comú.

A la primera arrel, he multiplicat l´index per #m1. Haig d'elevar el radicand #a1 a #m1

A la segon arrel, he multiplicat l´index per #m2. Haig d'elevar el radicand #a2 a #m2

]]> Les arrels ara són: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mroot»«/math»

Només cal multiplicar els radicands

]]> 1.1.3.90DT EXPONENT FRACCIONARI

Arrel i exponent fraccionari

L'arrel n-èsima d'un nombre es defineix així:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msup»«/math»

Qualsevol arrel es pot escriure com un exponent fraccionari

i viceversa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»5«/mn»«/msup»«mn mathvariant=¨bold¨»7«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mfrac bevelled=¨true¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»7«/mn»«/mfrac»«/msup»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.91Q D'arrel a fracció Escriu els exponents que corresponen a les arrels següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»y«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mroot»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 Exponent de x=#sol1Exponent de y=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>8</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>x</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>x</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>E</mi><mi>x</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>y</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'exponent de x, #n1, és el numerador de la fracció.

L'índex de l'arrel, #d1 és el denominador de la fracció.

L'exponent de y, #n2, és el numerador de la fracció.

L'índex de l'arrel, #d2 és el denominador de la fracció.

]]> 1.1.3.92Q De fracció a arrel Escriu les arrels que corresponen a les potències següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»y«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/msup»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 A=#sol1B=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n1</mi><mo><</mo><mi>d1</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msup><mi>x</mi><mfrac><mi>n1</mi><mi>d1</mi></mfrac></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n2</mi><mo><</mo><mi>d2</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msup><mi>y</mi><mfrac><mi>n2</mi><mi>d2</mi></mfrac></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mroot><mi>x</mi><mn>9</mn></mroot><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mroot><mi>y</mi><mn>7</mn></mroot><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>B</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El numerador de la fracció, #n1 és la potència de x. El denominador de la fracció, #d1 és l'índex de l'arrel.

El numerador de la fracció, #n2 és la potència de y. El denominador de la fracció, #d2 és l'índex de l'arrel.

]]> 1.1.3.95DT RADICALS EQUIVALENTS Radicals equivalents

Dos radicals són equivalents si els seus exponents fraccionaris són equivalents.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mn»6«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»perqu§#232;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.96Q RadicalsEquivalents? Els radicals següents són equivalents?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mroot»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mroot mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mroot»«/mstyle»«/math»

]]> 1.0000000 1.0000000 0 Vertader Fals Els radicands són «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«msup mathcolor=¨#000066¨»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«msup mathcolor=¨#000066¨»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mstyle»«/math»

Cal comparar les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>i1</mi><mo>,</mo><mi>e1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mfenced><mrow><mi>i1</mi><mo>></mo><mi>e1</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e1</mi></msup><mi>i1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msup><mi>a1</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msup><mi>a1</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>w1</mi><mo>*</mo><mi>i1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfenced><mrow><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w1</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mrow></mfenced><mo>*</mo><mi>e1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e2</mi></msup><mi>i2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfrac><mi>e2</mi><mi>e1</mi></mfrac><mo>=</mo><mi>w1</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>cert</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>fals</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>,</mo><mi>e1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>5</mn><mo>,</mo><mroot><mn>16807</mn><mn>12</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>,</mo><mi>i2</mi><mo>,</mo><mi>e2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>72</mn><mo>,</mo><mn>30</mn><mo>,</mo><mroot><mn>16807</mn><mn>12</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cert</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1.1.3.97Q RadicalsEquivalents?_2 Els radicals següents són equivalents?