# What is the square root of negative 8?

Mar 18, 2018

See a solution process below:

#### Explanation:

$\sqrt{8}$ can be rewritten as:

$\sqrt{4 \cdot 2 \cdot - 1}$

We can use this rule for radicals to simplify the expression:

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

$\sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{2} \cdot \textcolor{g r e e n}{- 1}} \implies$

$\sqrt{\textcolor{red}{4}} \cdot \sqrt{\textcolor{b l u e}{2}} \cdot \sqrt{\textcolor{g r e e n}{- 1}} \implies$

$2 \sqrt{\textcolor{b l u e}{2}} \cdot \sqrt{\textcolor{g r e e n}{- 1}}$

The symbol $i$ which is an imaginary number is another way to write: $\sqrt{- 1}$ so we can rewrite the expression as:

$2 \sqrt{\textcolor{b l u e}{2}} \cdot i \implies$

$2 i \sqrt{\textcolor{b l u e}{2}}$

If necessary we can approximate $\sqrt{2}$ as $1.414$ and get:

$2 \cdot 1.414 i \implies$

$2.828 i$