Question

Which expression is equivalent to StartFraction StartRoot 2 EndRoot Over RootIndex 3 StartRoot 2 EndRoot EndFraction?.

Answer 1

The expression is equivalent to $\sqrt[6]{2}$.

Given that

Expression; $\dfrac{\sqrt{2}}{\sqrt[3]{2} }$

We have to determine

The equivalent expression to the given expression.

According to the question

To determine the equivalent relation following all the steps given below.

Expression; $\dfrac{\sqrt{2}}{\sqrt[3]{2} }$

The equivalent expression is;

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

Hence, the expression is equivalent to $\sqrt[6]{2}$.

To know more about Expression click the link given below.

https://brainly.com/question/16450385