Evaluate square root of -360

$\sqrt{- 360}$

Step 1

Rewrite $- 360$ as $- 1 (360)$ .

$\sqrt{- 1 (360)}$

Step 2

Rewrite $\sqrt{- 1 (360)}$ as $\sqrt{- 1} \cdot \sqrt{360}$ .

$\sqrt{- 1} \cdot \sqrt{360}$

Step 3

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

$i \cdot \sqrt{360}$

Step 4

Rewrite $360$ as $6^{2} \cdot 10$ .

Factor $36$ out of $360$ .

$i \cdot \sqrt{36 (10)}$

Rewrite $36$ as $6^{2}$ .

$i \cdot \sqrt{6^{2} \cdot 10}$

Step 5

Pull terms out from under the radical.

$i \cdot (6 \sqrt{10})$

Step 6

Move $6$ to the left of $i$ .

$6 i \sqrt{10}$