Evaluate ( square root of -567)/( square root of -81)

$\frac{\sqrt{- 567}}{\sqrt{- 81}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 567$ as $- 1 (567)$ .

$\frac{\sqrt{- 1 (567)}}{\sqrt{- 81}}$

Rewrite $\sqrt{- 1 (567)}$ as $\sqrt{- 1} \cdot \sqrt{567}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{567}}{\sqrt{- 81}}$

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

$\frac{i \cdot \sqrt{567}}{\sqrt{- 81}}$

Rewrite $- 81$ as $- 1 (81)$ .

$\frac{i \cdot \sqrt{567}}{\sqrt{- 1 (81)}}$

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$\frac{i \cdot \sqrt{567}}{\sqrt{- 1} \cdot \sqrt{81}}$

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

$\frac{i \cdot \sqrt{567}}{i \cdot \sqrt{81}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{567}}{i \cdot \sqrt{81}}$

Rewrite the expression.

$\frac{\sqrt{567}}{\sqrt{81}}$

Step 3

Combine $\sqrt{567}$ and $\sqrt{81}$ into a single radical.

$\sqrt{\frac{567}{81}}$

Step 4

Divide $567$ by $81$ .

$\sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{7}$

Decimal Form:

$2.64575131 \dots$