Simplify square root of -112

$\sqrt{- 112}$

Step 1

Rewrite $- 112$ as $- 1 (112)$ .

$\sqrt{- 1 (112)}$

Step 2

Rewrite $\sqrt{- 1 (112)}$ as $\sqrt{- 1} \cdot \sqrt{112}$ .

$\sqrt{- 1} \cdot \sqrt{112}$

Step 3

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

$i \cdot \sqrt{112}$

Step 4

Rewrite $112$ as $4^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$i \cdot \sqrt{16 (7)}$

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

$i \cdot \sqrt{4^{2} \cdot 7}$

Step 5

Pull terms out from under the radical.

$i \cdot (4 \sqrt{7})$

Step 6

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

$4 i \sqrt{7}$