Evaluate square root of -160

$\sqrt{- 160}$

Step 1

Rewrite $- 160$ as $- 1 (160)$ .

$\sqrt{- 1 (160)}$

Step 2

Rewrite $\sqrt{- 1 (160)}$ as $\sqrt{- 1} \cdot \sqrt{160}$ .

$\sqrt{- 1} \cdot \sqrt{160}$

Step 3

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

$i \cdot \sqrt{160}$

Step 4

Rewrite $160$ as $4^{2} \cdot 10$ .

Factor $16$ out of $160$ .

$i \cdot \sqrt{16 (10)}$

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

$i \cdot \sqrt{4^{2} \cdot 10}$

Step 5

Pull terms out from under the radical.

$i \cdot (4 \sqrt{10})$

Step 6

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

$4 i \sqrt{10}$