Question

Which expression is equivalent to √10 over 4√8

4√200 over 2

4√20 over 2

2√5 over 5

100 over 8

Answer 1

Well, √10/4√8=​2 ​​4/​​3/​​​​​​√​10
so, i would have to say that 2√5 /5 would be the answer if my math is correct.​​​​​

Answer 2

Answer:

$\dfrac{\sqrt{10}}{\sqrt[4]{8}}\Rightarrow \dfrac{\sqrt[4]{200}}{2}$

A is correct.

Explanation:

Given: $\text{Expression: }\dfrac{\sqrt{10}}{\sqrt[4]{8}}$

We need to simplify the expression.

$\Rightarrow \dfrac{\sqrt{10}}{\sqrt[4]{8}}$

First we factor 8 and write as radical form.

$\Rightarrow \dfrac{\sqrt{10}}{\sqrt[4]{2^3}}$

$\Rightarrow \dfrac{10^{1/2}}{2^{3/4}}$

Rationalize the denominator

$\Rightarrow \dfrac{10^{1/2}\cdot 2^{1/4}}{2^{3/4}\cdot 2^{1/4}}$

$\Rightarrow \dfrac{10^{1/2}\cdot 2^{1/4}}{2^{4/4}}$

Make the radical of base 10 as 4

$\Rightarrow \dfrac{10^{2/4}\cdot 2^{1/4}}{2}$

$\Rightarrow \dfrac{100^{1/4}\cdot 2^{1/4}}{2}$

$\Rightarrow \dfrac{200^{1/4}}{2}$

$\Rightarrow \dfrac{\sqrt[4]{200}}{2}$

Hence, The equivalent expression is $\Rightarrow \dfrac{\sqrt[4]{200}}{2}$