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

`\frac{√(10)}{\sqrt[4]{8}}\Rightarrow \frac{\sqrt[4]{200}}{2}`

A is correct.

Explanation:

Given:
`\text{Expression: }\frac{√(10)}{\sqrt[4]{8}}`

We need to simplify the expression.

`\Rightarrow \frac{√(10)}{\sqrt[4]{8}}`

First we factor 8 and write as radical form.

`\Rightarrow \frac{√(10)}{\sqrt[4]{2^3}}`

`\Rightarrow (10^(1/2))/(2^(3/4))`

Rationalize the denominator

`\Rightarrow (10^(1/2)\cdot 2^(1/4))/(2^(3/4)\cdot 2^(1/4))`

`\Rightarrow (10^(1/2)\cdot 2^(1/4))/(2^(4/4))`

Make the radical of base 10 as 4

`\Rightarrow (10^(2/4)\cdot 2^(1/4))/(2)`

`\Rightarrow (100^(1/4)\cdot 2^(1/4))/(2)`

`\Rightarrow (200^(1/4))/(2)`

`\Rightarrow \frac{\sqrt[4]{200}}{2}`

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