Question

Raiz de 2 / raiz cubica de 2

Answer 1

$\dfrac{ \sqrt{2} }{ \sqrt[3]{2} } = \dfrac{ \sqrt{2}.\sqrt[3]{ 2^{2} } }{ \sqrt[3]{2}.\sqrt[3]{ 2^{2} } }= \dfrac{ \sqrt[6]{ 2^{3}} .\sqrt[6]{ 2^{4} } }{ \sqrt[3]{ 2^{3} } }= \dfrac{ \sqrt[6]{ 2^{3}.2^{4}} }{ 2 }= \dfrac{ \sqrt[6]{ 2^{7}} }{ 2 }= \dfrac{ 2\sqrt[6]{ 2} }{ 2 }=\sqrt[6]{ 2}$

Outra forma de resolver:

$\dfrac{ \sqrt{2} }{ \sqrt[3]{2} } = \dfrac{ \sqrt[6]{ 2^{3} } }{ \sqrt[6]{ 2^{2} } }= \sqrt[6]{ \dfrac{ 2^{3} }{ 2^{2} } }= \sqrt[6]{ 2^{3-2} } = \sqrt[6]{ 2^{1} } = \sqrt[6]{ 2 }$