Simplify square root of -90

$\sqrt{- 90}$

Step 1

Rewrite $- 90$ as $- 1 (90)$ .

$\sqrt{- 1 (90)}$

Step 2

Rewrite $\sqrt{- 1 (90)}$ as $\sqrt{- 1} \cdot \sqrt{90}$ .

$\sqrt{- 1} \cdot \sqrt{90}$

Step 3

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

$i \cdot \sqrt{90}$

Step 4

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$i \cdot \sqrt{9 (10)}$

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2} \cdot 10}$

Step 5

Pull terms out from under the radical.

$i \cdot (3 \sqrt{10})$

Step 6

Move $3$ to the left of $i$ .

$3 i \sqrt{10}$