Evaluate ( square root of -700)/( square root of -100)

$\frac{\sqrt{- 700}}{\sqrt{- 100}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 700$ as $- 1 (700)$ .

$\frac{\sqrt{- 1 (700)}}{\sqrt{- 100}}$

Rewrite $\sqrt{- 1 (700)}$ as $\sqrt{- 1} \cdot \sqrt{700}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{700}}{\sqrt{- 100}}$

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

$\frac{i \cdot \sqrt{700}}{\sqrt{- 100}}$

Rewrite $- 100$ as $- 1 (100)$ .

$\frac{i \cdot \sqrt{700}}{\sqrt{- 1 (100)}}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$\frac{i \cdot \sqrt{700}}{\sqrt{- 1} \cdot \sqrt{100}}$

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

$\frac{i \cdot \sqrt{700}}{i \cdot \sqrt{100}}$

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{700}}{i \cdot \sqrt{100}}$

Rewrite the expression.

$\frac{\sqrt{700}}{\sqrt{100}}$

Step 3

Combine $\sqrt{700}$ and $\sqrt{100}$ into a single radical.

$\sqrt{\frac{700}{100}}$

Step 4

Divide $700$ by $100$ .

$\sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{7}$

Decimal Form:

$2.64575131 \dots$