Simplify square root of -32

$\sqrt{- 32}$

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

$\sqrt{- 1 (32)}$

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

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

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

$i \cdot \sqrt{32}$

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

Factor $16$ out of $32$ .

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

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

$i \cdot \sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

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

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

$4 i \sqrt{2}$