Question

3. Escreva a expressão
na forma
de um único radical. Se possível, simpli-
fique a expressão.
​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Introduc_{\!\!,}\tilde ao~de~um~fator~externo~no~radicando}\\\huge\boxed{\boxed{\boxed{\boxed{\sf a\sqrt[\sf n]{\sf b}=\sqrt[\sf n]{\sf a^n\cdot b}}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\rm 3)~Escreva~a~express\tilde ao~\sqrt[\sf3]{\sf\dfrac{a}{b}\sqrt{\dfrac{a}{b}}}\\\rm na~forma~de~um~\acute unico~radical.\\\rm Se~poss\acute ivel~simplifique~a~express\tilde ao\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao}\\\sqrt[\sf3]{\sf\dfrac{a}{b}\sqrt{\dfrac{a}{b}}}=\sqrt[\sf3]{\sf\sqrt{\bigg(\dfrac{a}{b}\bigg)^2\cdot\dfrac{a}{b}}}\\\sf\sqrt[\sf3\cdot2]{\sf\bigg(\dfrac{a}{b}\bigg)^3}=\sqrt[\sf6\div3]{\sf\bigg(\dfrac{a}{b}\bigg)^{3\div3}}\\\sf\sqrt{\sf\dfrac{a}{b}}\end{array}}$