Pre-Algebra Examples

$\frac{\sqrt{- 40}}{\sqrt{- 5}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 40$ as $- 1 (40)$ .

$\frac{\sqrt{- 1 (40)}}{\sqrt{- 5}}$

Step 1.2

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{40}}{\sqrt{- 5}}$

Step 1.3

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

$\frac{i \cdot \sqrt{40}}{\sqrt{- 5}}$

Step 1.4

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

$\frac{i \cdot \sqrt{40}}{\sqrt{- 1 (5)}}$

Step 1.5

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

$\frac{i \cdot \sqrt{40}}{\sqrt{- 1} \cdot \sqrt{5}}$

Step 1.6

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

$\frac{i \cdot \sqrt{40}}{i \cdot \sqrt{5}}$

Step 2

Cancel the common factor of $i$ .

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Step 2.1

Cancel the common factor.

$\frac{i \cdot \sqrt{40}}{i \cdot \sqrt{5}}$

Step 2.2

Rewrite the expression.

$\frac{\sqrt{40}}{\sqrt{5}}$

Step 3

Combine $\sqrt{40}$ and $\sqrt{5}$ into a single radical.

$\sqrt{\frac{40}{5}}$

Step 4

Divide $40$ by $5$ .

$\sqrt{8}$

Step 5

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

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Step 5.1

Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

Step 5.2

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:

$2.82842712 \dots$