Evaluate ( square root of -72)/( square root of -6)

$\frac{\sqrt{- 72}}{\sqrt{- 6}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 72$ as $- 1 (72)$ .

$\frac{\sqrt{- 1 (72)}}{\sqrt{- 6}}$

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{72}}{\sqrt{- 6}}$

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

$\frac{i \cdot \sqrt{72}}{\sqrt{- 6}}$

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{i \cdot \sqrt{72}}{\sqrt{- 1 (6)}}$

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$\frac{i \cdot \sqrt{72}}{\sqrt{- 1} \cdot \sqrt{6}}$

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

$\frac{i \cdot \sqrt{72}}{i \cdot \sqrt{6}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{72}}{i \cdot \sqrt{6}}$

Rewrite the expression.

$\frac{\sqrt{72}}{\sqrt{6}}$

Step 3

Combine $\sqrt{72}$ and $\sqrt{6}$ into a single radical.

$\sqrt{\frac{72}{6}}$

Step 4

Divide $72$ by $6$ .

$\sqrt{12}$

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:

$3.46410161 \dots$