# What is the square root of 8/18?

Apr 4, 2018

$\frac{2}{3}$

#### Explanation:

We want $\sqrt{\frac{8}{18}}$

Recalling that $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} ,$ we get

$\frac{\sqrt{8}}{\sqrt{18}}$

We need to simplify these roots.

$\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \sqrt{2} = 2 \sqrt{2}$

$\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \sqrt{2} = 3 \sqrt{2}$

So, we then have

$\frac{2 \cancel{\sqrt{2}}}{3 \cancel{\sqrt{2}}} = \frac{2}{3}$