Evaluate ( square root of -405)/( square root of -81)

$\frac{\sqrt{- 405}}{\sqrt{- 81}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 405$ as $- 1 (405)$ .

$\frac{\sqrt{- 1 (405)}}{\sqrt{- 81}}$

Rewrite $\sqrt{- 1 (405)}$ as $\sqrt{- 1} \cdot \sqrt{405}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{405}}{\sqrt{- 81}}$

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

$\frac{i \cdot \sqrt{405}}{\sqrt{- 81}}$

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

$\frac{i \cdot \sqrt{405}}{\sqrt{- 1 (81)}}$

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

$\frac{i \cdot \sqrt{405}}{\sqrt{- 1} \cdot \sqrt{81}}$

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

$\frac{i \cdot \sqrt{405}}{i \cdot \sqrt{81}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{405}}{i \cdot \sqrt{81}}$

Rewrite the expression.

$\frac{\sqrt{405}}{\sqrt{81}}$

Step 3

Combine $\sqrt{405}$ and $\sqrt{81}$ into a single radical.

$\sqrt{\frac{405}{81}}$

Step 4

Divide $405$ by $81$ .

$\sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$