Evaluate - square root of -45

$- \sqrt{- 45}$

Step 1

Rewrite $- 45$ as $- 1 (45)$ .

$- \sqrt{- 1 (45)}$

Step 2

Rewrite $\sqrt{- 1 (45)}$ as $\sqrt{- 1} \cdot \sqrt{45}$ .

$- (\sqrt{- 1} \cdot \sqrt{45})$

Step 3

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

$- (i \cdot \sqrt{45})$

Step 4

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$- (i \cdot \sqrt{9 (5)})$

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Simplify the expression.

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

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

Multiply $3$ by $- 1$ .

$- 3 i \sqrt{5}$