Finite Math Examples

$\frac{\sqrt{- 14}}{\sqrt{- 7}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 14$ as $- 1 (14)$ .

$\frac{\sqrt{- 1 (14)}}{\sqrt{- 7}}$

Step 1.2

Rewrite $\sqrt{- 1 (14)}$ as $\sqrt{- 1} \cdot \sqrt{14}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{14}}{\sqrt{- 7}}$

Step 1.3

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

$\frac{i \cdot \sqrt{14}}{\sqrt{- 7}}$

Step 1.4

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{i \cdot \sqrt{14}}{\sqrt{- 1 (7)}}$

Step 1.5

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$\frac{i \cdot \sqrt{14}}{\sqrt{- 1} \cdot \sqrt{7}}$

Step 1.6

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

$\frac{i \cdot \sqrt{14}}{i \cdot \sqrt{7}}$

Step 2

Cancel the common factor of $i$ .

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Step 2.1

Cancel the common factor.

$\frac{i \cdot \sqrt{14}}{i \cdot \sqrt{7}}$

Step 2.2

Rewrite the expression.

$\frac{\sqrt{14}}{\sqrt{7}}$

Step 3

Combine $\sqrt{14}$ and $\sqrt{7}$ into a single radical.

$\sqrt{\frac{14}{7}}$

Step 4

Divide $14$ by $7$ .

$\sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$