Evaluate square root of -40

$\sqrt{- 40}$

Step 1

Rewrite $- 40$ as $- 1 (40)$ .

$\sqrt{- 1 (40)}$

Step 2

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

$\sqrt{- 1} \cdot \sqrt{40}$

Step 3

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

$i \cdot \sqrt{40}$

Step 4

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

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

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

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

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{10})$

Step 6

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

$2 i \sqrt{10}$