Simplify square root of -54

$\sqrt{- 54}$

Rewrite $- 54$ as $- 1 (54)$ .

$\sqrt{- 1 (54)}$

Rewrite $\sqrt{- 1 (54)}$ as $\sqrt{- 1} \cdot \sqrt{54}$ .

$\sqrt{- 1} \cdot \sqrt{54}$

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

$i \cdot \sqrt{54}$

Rewrite $54$ as $3^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$i \cdot \sqrt{9 (6)}$

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

$i \cdot \sqrt{3^{2} \cdot 6}$

Pull terms out from under the radical.

$i \cdot (3 \sqrt{6})$

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

$3 i \sqrt{6}$