# How do you simplify Square root of (-16/25)??

Mar 11, 2018

The expression is equal to $\frac{4 i}{5}$.

#### Explanation:

$\sqrt{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}} = \frac{\sqrt{\textcolor{red}{a}}}{\sqrt{\textcolor{b l u e}{b}}}$

$\sqrt{{\textcolor{red}{a}}^{2}} = \textcolor{red}{a}$

$\sqrt{{\textcolor{red}{a}}^{2} \cdot \textcolor{b l u e}{b}} = \textcolor{red}{a} \sqrt{\textcolor{b l u e}{b}}$

$\sqrt{- 1} = i$

Now here's the actual expression:

$\textcolor{w h i t e}{=} \sqrt{- \frac{16}{25}}$

$= \sqrt{\frac{- 16}{25}}$

$= \frac{\sqrt{- 16}}{\sqrt{25}}$

$= \frac{\sqrt{4 \cdot 4 \cdot - 1}}{\sqrt{5 \cdot 5}}$

$= \frac{\sqrt{{4}^{2} \cdot - 1}}{\sqrt{{5}^{2}}}$

$= \frac{4 \sqrt{- 1}}{5}$

$= \frac{4 i}{5}$