Question

Which expression is equivalent to StartFraction StartRoot 2 EndRoot Over RootIndex 3 StartRoot 2 EndRoot EndFraction? One-fourth RootIndex 6 StartRoot 2 EndRoot StartRoot 2 EndRoot StartFraction StartRoot 2 EndRoot Over 2 EndFraction


Answer is RootIndex 6 StartRoot 2 EndRoot B on edg

Answer 1

Question:

Which expression is equivalent to

$\frac{\sqrt{2}}{\sqrt[3]{2}}$

Answer:

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

Step-by-step explanation:

Given

$\frac{\sqrt{2}}{\sqrt[3]{2}}$

Required

Simplify

From laws of indices;

$\sqrt[n]{x} =x^{\frac{1}{n}}$

So, the expression can be rewritten as

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

Also, from laws of indices

$\frac{x^a}{x^b} = x^{a-b}$

So, the expression is further solved to:

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

Solve exponents as fraction

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

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

This can be rewritten as

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

Answer 2

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

Given expression is,  $\frac{\sqrt{2} }{\sqrt[3]{2} }$

Expression can be written as,

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

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