Simplify - square root of -20

$- \sqrt{- 20}$

Step 1

Rewrite $- 20$ as $- 1 (20)$ .

$- \sqrt{- 1 (20)}$

Step 2

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$- (\sqrt{- 1} \cdot \sqrt{20})$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$- (i \cdot \sqrt{20})$

Step 4

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$- (i \cdot \sqrt{4 (5)})$

Rewrite $4$ as $2^{2}$ .

$- (i \cdot \sqrt{2^{2} \cdot 5})$

Step 5

Pull terms out from under the radical.

$- (i \cdot (2 \sqrt{5}))$

Step 6

Simplify the expression.

Move $2$ to the left of $i$ .

$- (2 \cdot i \sqrt{5})$

Multiply $2$ by $- 1$ .

$- 2 i \sqrt{5}$