Question

Racionalize os denominadores 8/³raiz de 27

Answer 1

$\large\boxed{\begin{array}{l}\sf radical:\sqrt[\sf n]{\sf a^m}\longrightarrow fator\,racionalizante:\sqrt[\sf n]{\sf a^{m-n}}\\\sf radical:\sqrt[\sf3]{\sf27}\longrightarrow fator\,racionalizante:\sqrt[\sf3]{\sf27^{3-1}}=\sqrt[\sf3]{\sf27^2}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\dfrac{8}{\sqrt[\sf3]{\sf27}}\cdot\dfrac{\sqrt[\sf3]{\sf27^2}}{\sqrt[\sf3]{\sf27^2}}=\dfrac{8\sqrt[\sf3]{\sf27^2}}{\sqrt[\sf3]{\sf27^3}}=\dfrac{8\sqrt[\sf3]{\sf27^2}}{27}\end{array}}$