Simplify the Radical Expression square root of -18

$\sqrt{- 18}$

Step 1

Rewrite $- 18$ as $- 1 (18)$ .

$\sqrt{- 1 (18)}$

Step 2

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$\sqrt{- 1} \cdot \sqrt{18}$

Step 3

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

$i \cdot \sqrt{18}$

Step 4

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$i \cdot \sqrt{9 (2)}$

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

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

Step 5

Pull terms out from under the radical.

$i \cdot (| 3 | \sqrt{2})$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$i \cdot (3 \sqrt{2})$

Step 7

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

$3 i \sqrt{2}$