# How do you simplify sqrt0.08?

Mar 16, 2016

You may begin by writing $\sqrt{0.08} = \sqrt{\frac{8}{100}}$

#### Explanation:

Then we apply the 'radical rules':
$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ and $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$

Translated to our problem:
$= \frac{\sqrt{8}}{\sqrt{100}} = \frac{\sqrt{8}}{\sqrt{{10}^{2}}} = \frac{\sqrt{8}}{10}$

But since $8 = 4 \times 2 = {2}^{2} \times 2$:
$\to \sqrt{8} = \sqrt{{2}^{2}} \times \sqrt{2} = 2 \sqrt{2}$

Then we get to:
$= \frac{2 \sqrt{2}}{10} = \frac{1}{5} \sqrt{2}$