Simplify square root of -56

$\sqrt{- 56}$

Rewrite $- 56$ as $- 1 (56)$ .

$\sqrt{- 1 (56)}$

Rewrite $\sqrt{- 1 (56)}$ as $\sqrt{- 1} \cdot \sqrt{56}$ .

$\sqrt{- 1} \cdot \sqrt{56}$

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

$i \cdot \sqrt{56}$

Rewrite $56$ as $2^{2} \cdot 14$ .

Factor $4$ out of $56$ .

$i \cdot \sqrt{4 (14)}$

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

$i \cdot \sqrt{2^{2} \cdot 14}$

Pull terms out from under the radical.

$i \cdot (2 \sqrt{14})$

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

$2 i \sqrt{14}$