4t ESO/4.01 NOMBRES/4.01.3 Nombres irracionals 4.01.3.33 CàlculsIrracionals DiagonalQuadrat Quant mesura la diagonal d'un quadrat de costat #a?

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"><mi>a</mi><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mrow><mn>2</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt></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>57</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"><mn>57</mn><mo>*</mo><msqrt><mn>2</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</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 la diagonal és la hipotenusa del triangle rectangle, cal aplicar el teorema de Pitàgores «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»=«/mo»«msqrt»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mfenced»«/math»; els catets b i c són tots dos iguals a #a.

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