Simplify square root of -80

$\sqrt{- 80}$

Step 1

Rewrite $- 80$ as $- 1 (80)$ .

$\sqrt{- 1 (80)}$

Step 2

Rewrite $\sqrt{- 1 (80)}$ as $\sqrt{- 1} \cdot \sqrt{80}$ .

$\sqrt{- 1} \cdot \sqrt{80}$

Step 3

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

$i \cdot \sqrt{80}$

Step 4

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$i \cdot \sqrt{16 (5)}$

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

$i \cdot \sqrt{4^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$i \cdot (4 \sqrt{5})$

Step 6

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

$4 i \sqrt{5}$