Question

racionalize
$\frac{2\sqrt{2} }{\sqrt[3]{2} }$
a resposta é $\sqrt[6]{2^{7} }$ ?

Answer 1

Resposta:

$\frac{2\sqrt{2}}{\sqrt[3]{2}}=\frac{2.2^{1/2}}{2^{1/3}}=\frac{2^{1+1/2}}{2^{1/3}}=\frac{2^{3/2}}{2^{1/3}} =2^{3/2-1/3} =\\ \\ 2^{(9-2)/6}=2^{7/6}=\sqrt[6]{2^{7}}$

$Sim.~A~resposta~e~~\sqrt[6]{2^{7} }$