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

Answer:

B. 6 StartRoot 2 EndRoot

Step-by-step explanation:

Edge 2020

Answer 2

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

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