Question

$\sqrt{ \frac{4}{ \sqrt{2} } } =?$ como resolver raiz deste tipo?

Answer 1

$\boxed{ \sqrt{\frac{4}{ \sqrt{2} }}=\frac{ \sqrt{4} }{ \sqrt{ \sqrt{2} } }=\frac{2}{ \sqrt[4]{2} } =\frac{2^1}{2^{\frac{1}{4}}}=2^{1-\frac{1}{4}}=2^{\frac{3}{4}}= \sqrt[4]{2^3}= \sqrt[4]{8} }$

Answer 2

Raiz do quociente.

$\boxed{ \sqrt{ \frac{4}{ \sqrt{2} } } ~\to~ \frac{ \sqrt{4} }{ \sqrt[4]{2} } ~\to~ \frac{2}{2^{ \frac{1}{4} }} ~\to~2^{ \frac{3}{4} }~\to~2^{ \frac{3}{4} }~\to~ \sqrt[4]{2^3}}$