Evaluate - square root of -12

$- \sqrt{- 12}$

Step 1

Rewrite $- 12$ as $- 1 (12)$ .

$- \sqrt{- 1 (12)}$

Step 2

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$- (\sqrt{- 1} \cdot \sqrt{12})$

Step 3

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

$- (i \cdot \sqrt{12})$

Step 4

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$- (i \cdot \sqrt{4 (3)})$

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

$- (i \cdot \sqrt{2^{2} \cdot 3})$

Step 5

Pull terms out from under the radical.

$- (i \cdot (2 \sqrt{3}))$

Step 6

Simplify the expression.

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

$- (2 \cdot i \sqrt{3})$

Multiply $2$ by $- 1$ .

$- 2 i \sqrt{3}$