# How do you simplify sqrt(5) / sqrt(8)?

May 13, 2016

$\frac{\sqrt{10}}{4}$

#### Explanation:

Given:$\text{ } \frac{\sqrt{5}}{\sqrt{8}}$

Multiply by 1 but in the form of $1 = \frac{\sqrt{8}}{\sqrt{8}}$

$\text{ } = \frac{\sqrt{5}}{\sqrt{8}} \times \frac{\sqrt{8}}{\sqrt{8}}$

$\text{ } = \frac{\sqrt{5} \sqrt{8}}{8}$

But $8$ is the same as ${2}^{2} \times 2 \text{ so } \sqrt{8} = 2 \sqrt{2}$

$\text{ "=(2sqrt(5)sqrt(2))/8 " "=" } \frac{\sqrt{5 \times 2}}{4}$

$\text{ } = \frac{\sqrt{10}}{4}$