Simplify square root of -150

$\sqrt{- 150}$

Step 1

Rewrite $- 150$ as $- 1 (150)$ .

$\sqrt{- 1 (150)}$

Step 2

Rewrite $\sqrt{- 1 (150)}$ as $\sqrt{- 1} \cdot \sqrt{150}$ .

$\sqrt{- 1} \cdot \sqrt{150}$

Step 3

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

$i \cdot \sqrt{150}$

Step 4

Rewrite $150$ as $5^{2} \cdot 6$ .

Factor $25$ out of $150$ .

$i \cdot \sqrt{25 (6)}$

Rewrite $25$ as $5^{2}$ .

$i \cdot \sqrt{5^{2} \cdot 6}$

Step 5

Pull terms out from under the radical.

$i \cdot (5 \sqrt{6})$

Step 6

Move $5$ to the left of $i$ .

$5 i \sqrt{6}$