Evaluate ( square root of -80)/( square root of -10)

$\frac{\sqrt{- 80}}{\sqrt{- 10}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 80$ as $- 1 (80)$ .

$\frac{\sqrt{- 1 (80)}}{\sqrt{- 10}}$

Rewrite $\sqrt{- 1 (80)}$ as $\sqrt{- 1} \cdot \sqrt{80}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{80}}{\sqrt{- 10}}$

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

$\frac{i \cdot \sqrt{80}}{\sqrt{- 10}}$

Rewrite $- 10$ as $- 1 (10)$ .

$\frac{i \cdot \sqrt{80}}{\sqrt{- 1 (10)}}$

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$\frac{i \cdot \sqrt{80}}{\sqrt{- 1} \cdot \sqrt{10}}$

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

$\frac{i \cdot \sqrt{80}}{i \cdot \sqrt{10}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{80}}{i \cdot \sqrt{10}}$

Rewrite the expression.

$\frac{\sqrt{80}}{\sqrt{10}}$

Step 3

Combine $\sqrt{80}$ and $\sqrt{10}$ into a single radical.

$\sqrt{\frac{80}{10}}$

Step 4

Divide $80$ by $10$ .

$\sqrt{8}$

Step 5

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

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

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

Step 6

Pull terms out from under the radical.

$2 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$