Evaluate ( square root of -54)/( square root of -6)

$\frac{\sqrt{- 54}}{\sqrt{- 6}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 54$ as $- 1 (54)$ .

$\frac{\sqrt{- 1 (54)}}{\sqrt{- 6}}$

Rewrite $\sqrt{- 1 (54)}$ as $\sqrt{- 1} \cdot \sqrt{54}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{54}}{\sqrt{- 6}}$

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

$\frac{i \cdot \sqrt{54}}{\sqrt{- 6}}$

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

$\frac{i \cdot \sqrt{54}}{\sqrt{- 1 (6)}}$

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

$\frac{i \cdot \sqrt{54}}{\sqrt{- 1} \cdot \sqrt{6}}$

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

$\frac{i \cdot \sqrt{54}}{i \cdot \sqrt{6}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{54}}{i \cdot \sqrt{6}}$

Rewrite the expression.

$\frac{\sqrt{54}}{\sqrt{6}}$

Step 3

Combine $\sqrt{54}$ and $\sqrt{6}$ into a single radical.

$\sqrt{\frac{54}{6}}$

Step 4

Simplify the expression.

Divide $54$ by $6$ .

$\sqrt{9}$

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

$\sqrt{3^{2}}$

Step 5

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

$3$