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.

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

Simplify the expression.

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

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

Multiply $3$ by $- 1$ .

$- 3 i \sqrt{6}$