# How do you simplify sqrt(-9)?

Mar 25, 2018

The expression is equal to $3 i$.

#### Explanation:

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

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

And also the definition of the imaginary number:

$\sqrt{- 1} = i$

Here are these properties applied to our expression.

$\textcolor{w h i t e}{=} \sqrt{- 9}$

$= \sqrt{- 3 \cdot 3}$

$= \sqrt{- 1 \cdot 3 \cdot 3}$

$= \sqrt{- 1 \cdot {3}^{2}}$

$= \sqrt{- 1} \cdot \sqrt{{3}^{2}}$

$= \sqrt{- 1} \cdot 3$

$= i \cdot 3$

$= 3 i$

This is the result. Hope this helped!

Mar 25, 2018

$\sqrt{- 9} = 3 i$

#### Explanation:

Given:

$\sqrt{- 9}$

$\sqrt{{3}^{2} \times - 1}$
Apply rule: $\sqrt{{a}^{2}} = a$, and $\sqrt{- 1} = i$.
$3 i$