Finite Math Examples

$\frac{\sqrt{- 500}}{\sqrt{- 5}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 500$ as $- 1 (500)$ .

$\frac{\sqrt{- 1 (500)}}{\sqrt{- 5}}$

Step 1.2

Rewrite $\sqrt{- 1 (500)}$ as $\sqrt{- 1} \cdot \sqrt{500}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{500}}{\sqrt{- 5}}$

Step 1.3

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

$\frac{i \cdot \sqrt{500}}{\sqrt{- 5}}$

Step 1.4

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{i \cdot \sqrt{500}}{\sqrt{- 1 (5)}}$

Step 1.5

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$\frac{i \cdot \sqrt{500}}{\sqrt{- 1} \cdot \sqrt{5}}$

Step 1.6

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

$\frac{i \cdot \sqrt{500}}{i \cdot \sqrt{5}}$

Step 2

Cancel the common factor of $i$ .

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Step 2.1

Cancel the common factor.

$\frac{i \cdot \sqrt{500}}{i \cdot \sqrt{5}}$

Step 2.2

Rewrite the expression.

$\frac{\sqrt{500}}{\sqrt{5}}$

Step 3

Combine $\sqrt{500}$ and $\sqrt{5}$ into a single radical.

$\sqrt{\frac{500}{5}}$

Step 4

Simplify the expression.

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Step 4.1

Divide $500$ by $5$ .

$\sqrt{100}$

Step 4.2

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

Step 4.3

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

$10$