Question

Racionalize a fração:

a/3√b

(a sobre raiz cúbica de b)

Answer 1

Resposta:

$\frac{a}{ \sqrt[3]{b} } = \frac{a \sqrt[3]{b} }{\sqrt[3]{b^2}}$

Answer 2

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$\large\boxed{\begin{array}{l}\sf Dada~a~express\tilde ao~\sqrt[\sf n]{\sf a^m}~o~fator~racionalizante~\acute e~dado~por\\\sf\sqrt[\sf n]{\sf a^{n-m}}.\\\underline{\rm prova\!:}\\\sf \sqrt[\sf n]{\sf a^m}\cdot\sqrt[\sf n]{\sf a^{n-m}}=\sqrt[\sf n]{\sf a^m\cdot a^{n-m}}\\\sf \sqrt[\sf n]{\sf a^m}\cdot\sqrt[\sf n]{\sf a^{n-m}}=\sqrt[\sf n]{\sf a^{\backslash\!\!\!m+n-\backslash\!\!\!m}}=\sqrt[\sf \backslash\!\!\!n]{\sf a^{\backslash\!\!\!n}}=a~~\blacksquare\end{array}}$

$\sf\dfrac{a}{\sqrt[\sf3]{\sf b}}\\\underline{\rm c\acute alculo~do~fator~racionalizante\!:}\\\sf \sqrt[\sf3]{\sf b^{3-1}}=\sqrt[\sf3]{\sf b^2}\\\underline{\rm multiplicando~e~dividindo~a~express\tilde ao}\\\underline{\rm pelo~fator~racionalizante~temos\!:}\\\sf\dfrac{a}{\sqrt[\sf3]{\sf b}}\cdot\dfrac{\sqrt[\sf3]{\sf b^2}}{\sqrt[\sf3]{\sf b^2}}=\dfrac{a\sqrt[\sf3]{\sf b^2}}{\sqrt[\sf3]{\sf b^{1+2}}}\\\sf\dfrac{a\sqrt[\sf3]{\sf b^2}}{\sqrt[\sf\backslash\!\!\!3]{\sf b^{\backslash\!\!\!3}}}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf\dfrac{a}{\sqrt[\sf3]{\sf b}}=\dfrac{a\sqrt[\sf3]{\sf b^2}}{b}}}}}}}}$