How do you simplify: the square root of -500?

Apr 15, 2018

$10 i \sqrt{5}$

Explanation:

$\sqrt{- 500} = \sqrt{100 \cdot - 5}$

Recalling that $\sqrt{a \cdot b} = \sqrt{a} \sqrt{b} ,$ we obtain

$\sqrt{100} \cdot \sqrt{- 5} = 10 \sqrt{- 5}$

$10 \sqrt{- 5} = 10 \sqrt{- 1} \sqrt{5}$

$i = \sqrt{- 1} ,$ so we may rewrite as

$10 i \sqrt{5}$