Evaluate square root of -76

$\sqrt{- 76}$

Step 1

Rewrite $- 76$ as $- 1 (76)$ .

$\sqrt{- 1 (76)}$

Step 2

Rewrite $\sqrt{- 1 (76)}$ as $\sqrt{- 1} \cdot \sqrt{76}$ .

$\sqrt{- 1} \cdot \sqrt{76}$

Step 3

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

$i \cdot \sqrt{76}$

Step 4

Rewrite $76$ as $2^{2} \cdot 19$ .

Factor $4$ out of $76$ .

$i \cdot \sqrt{4 (19)}$

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

$i \cdot \sqrt{2^{2} \cdot 19}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{19})$

Step 6

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

$2 i \sqrt{19}$