# How do you find the square root of -300?

Mar 30, 2018

See a solution process below:

#### Explanation:

First, we can rewrite this expression as:

$\sqrt{- 300} \implies \sqrt{100 \cdot 3 \cdot - 1}$

Next, we can use this rule of radicals to simplify the expression as:

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

$\sqrt{\textcolor{red}{100} \cdot \textcolor{b l u e}{3} \cdot \textcolor{g r e e n}{- 1}} \implies$

$\sqrt{\textcolor{red}{100}} \cdot \sqrt{\textcolor{b l u e}{3}} \cdot \sqrt{\textcolor{g r e e n}{- 1}} \implies$

color(red)(10)sqrt(color(blue)(3))sqrt(color(green)(-1)

The square root of negative 1 is called an imaginary number and can be represented by $i$.

We can rewrite the expression as:

$\textcolor{red}{10} \sqrt{\textcolor{b l u e}{3}} \sqrt{\textcolor{g r e e n}{- 1}} \implies$

$\textcolor{red}{10} \sqrt{\textcolor{b l u e}{3}} \textcolor{g r e e n}{i}$

Or

$\textcolor{red}{10} \textcolor{g r e e n}{i} \sqrt{\textcolor{b l u e}{3}}$