Simplify the Radical Expression - square root of -4

$- \sqrt{- 4}$

Rewrite $- 4$ as $- 1 (4)$ .

$- \sqrt{- 1 (4)}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$- (\sqrt{- 1} \cdot \sqrt{4})$

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

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

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

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

Pull terms out from under the radical.

$- (i \cdot | 2 |)$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- (i \cdot 2)$

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

$- (2 \cdot i)$

Multiply $2$ by $- 1$ .

$- 2 i$