# How do you simplify sqrt(.0001)?

Jan 24, 2016

$\sqrt{0.0001} = 0.01$

#### Explanation:

Using the properties of square roots that

• $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ if $a \ge 0$, $b > 0$
• $\sqrt{{a}^{2}} = | a |$ for $a \in \mathbb{R}$

we have

$\sqrt{0.0001} = \sqrt{\frac{1}{10000}}$

$= \frac{\sqrt{1}}{\sqrt{10000}}$

$= \frac{\sqrt{{1}^{2}}}{\sqrt{{100}^{2}}}$

$= | 1 \frac{|}{|} 100 |$

$= \frac{1}{100}$

$= 0.01$