How do you simplify: the square root of -125?

Jul 16, 2015

$5 i \cdot \sqrt{5}$

Explanation:

Let's break this into it's factors:

$\sqrt{- 125} = \sqrt{- 1 \cdot 5 \cdot 5 \cdot 5} = \sqrt{- 1} \cdot \sqrt{5} \cdot \sqrt{{5}^{2}}$

We can evaluate the first and 3rd terms here to give:
$\sqrt{- 1} \cdot \sqrt{5} \cdot \sqrt{{5}^{2}} = 5 i \cdot \sqrt{5}$

Where $i = \sqrt{- 1}$ (a concept from complex analysis).