Simplify ( square root of -36)/(- square root of 4)

$\frac{\sqrt{- 36}}{- \sqrt{4}}$

Pull out imaginary unit $i$ .

Rewrite $- 36$ as $- 1 (36)$ .

$\frac{\sqrt{- 1 (36)}}{- \sqrt{4}}$

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{36}}{- \sqrt{4}}$

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

$\frac{i \cdot \sqrt{36}}{- \sqrt{4}}$

Combine $\sqrt{36}$ and $\sqrt{4}$ into a single radical.

$\frac{i \cdot \sqrt{\frac{36}{4}}}{- 1}$

Cancel the common factor of $36$ and $4$ .

Factor $4$ out of $36$ .

$\frac{i \cdot \sqrt{\frac{4 \cdot 9}{4}}}{- 1}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{i \cdot \sqrt{\frac{4 \cdot 9}{4 (1)}}}{- 1}$

Cancel the common factor.

$\frac{i \cdot \sqrt{\frac{4 \cdot 9}{4 \cdot 1}}}{- 1}$

Rewrite the expression.

$\frac{i \cdot \sqrt{\frac{9}{1}}}{- 1}$

Divide $9$ by $1$ .

$\frac{i \cdot \sqrt{9}}{- 1}$

Simplify the expression.

Move the negative one from the denominator of $\frac{i \cdot \sqrt{9}}{- 1}$ .

$- 1 \cdot (i \cdot \sqrt{9})$

Rewrite $- 1 \cdot (i \cdot \sqrt{9})$ as $- (i \cdot \sqrt{9})$ .

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

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

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

Pull terms out from under the radical, assuming positive real numbers.

$- (i \cdot 3)$

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

$- (3 \cdot i)$

Multiply $3$ by $- 1$ .

$- 3 i$