Simplify - square root of -32

$- \sqrt{- 32}$

Step 1

Rewrite $- 32$ as $- 1 (32)$ .

$- \sqrt{- 1 (32)}$

Step 2

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$- (\sqrt{- 1} \cdot \sqrt{32})$

Step 3

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

$- (i \cdot \sqrt{32})$

Step 4

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$- (i \cdot \sqrt{16 (2)})$

Rewrite $16$ as $4^{2}$ .

$- (i \cdot \sqrt{4^{2} \cdot 2})$

Step 5

Pull terms out from under the radical.

$- (i \cdot (4 \sqrt{2}))$

Step 6

Simplify the expression.

Move $4$ to the left of $i$ .

$- (4 \cdot i \sqrt{2})$

Multiply $4$ by $- 1$ .

$- 4 i \sqrt{2}$