Evaluate ( square root of -36)/( square root of -3)

$\frac{\sqrt{- 36}}{\sqrt{- 3}}$

Step 1

Pull out imaginary unit $i$ .

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

$\frac{\sqrt{- 1 (36)}}{\sqrt{- 3}}$

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

$\frac{\sqrt{- 1} \cdot \sqrt{36}}{\sqrt{- 3}}$

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

$\frac{i \cdot \sqrt{36}}{\sqrt{- 3}}$

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{i \cdot \sqrt{36}}{\sqrt{- 1 (3)}}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$\frac{i \cdot \sqrt{36}}{\sqrt{- 1} \cdot \sqrt{3}}$

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

$\frac{i \cdot \sqrt{36}}{i \cdot \sqrt{3}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{36}}{i \cdot \sqrt{3}}$

Rewrite the expression.

$\frac{\sqrt{36}}{\sqrt{3}}$

Step 3

Combine $\sqrt{36}$ and $\sqrt{3}$ into a single radical.

$\sqrt{\frac{36}{3}}$

Step 4

Divide $36$ by $3$ .

$\sqrt{12}$

Step 5

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3)}$

Rewrite $4$ as $2^{2}$ .

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

Step 6

Pull terms out from under the radical.

$2 \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3}$

Decimal Form:

$3.46410161 \dots$