# What is the square root of -72?

Sep 21, 2015

$= 6 i \sqrt{2}$

#### Explanation:

-72 doesn't actually have a real square root, but it does have an imaginary one.

$\sqrt{- 72}$
$= \sqrt{- 1 \cdot 8 \cdot 9}$
$= \sqrt{- 1 \cdot {2}^{2} \cdot 2 \cdot {3}^{2}}$
$= \left(2 \cdot 3\right) \sqrt{- 1 \cdot 2}$
$= 6 \sqrt{- 1 \cdot 2}$

We will be able to bring out -1, by denoting it as $i$.

$= 6 \sqrt{- 1 \cdot 2}$
$= 6 i \sqrt{2}$
=