Evaluate square root of -120

$\sqrt{- 120}$

Step 1

Rewrite $- 120$ as $- 1 (120)$ .

$\sqrt{- 1 (120)}$

Step 2

Rewrite $\sqrt{- 1 (120)}$ as $\sqrt{- 1} \cdot \sqrt{120}$ .

$\sqrt{- 1} \cdot \sqrt{120}$

Step 3

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

$i \cdot \sqrt{120}$

Step 4

Rewrite $120$ as $2^{2} \cdot 30$ .

Factor $4$ out of $120$ .

$i \cdot \sqrt{4 (30)}$

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

$i \cdot \sqrt{2^{2} \cdot 30}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{30})$

Step 6

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

$2 i \sqrt{30}$