Evaluate - square root of -4

$- \sqrt{- 4}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$- (i \cdot 2)$

Step 6

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

$- (2 \cdot i)$

Step 7

Multiply $2$ by $- 1$ .

$- 2 i$