Simplify - square root of -75

$- \sqrt{- 75}$

Rewrite $- 75$ as $- 1 (75)$ .

$- \sqrt{- 1 (75)}$

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$- (\sqrt{- 1} \cdot \sqrt{75})$

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

$- (i \cdot \sqrt{75})$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$- (i \cdot \sqrt{25 (3)})$

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

$- (i \cdot \sqrt{5^{2} \cdot 3})$

Pull terms out from under the radical.

$- (i \cdot (5 \sqrt{3}))$

Simplify the expression.

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

$- (5 \cdot i \sqrt{3})$

Multiply $5$ by $- 1$ .

$- 5 i \sqrt{3}$