Algebra Examples

$\frac{\sqrt{- 32}}{\sqrt{- 50}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 32$ as $- 1 (32)$ .

$\frac{\sqrt{- 1 (32)}}{\sqrt{- 50}}$

Step 1.2

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{32}}{\sqrt{- 50}}$

Step 1.3

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

$\frac{i \cdot \sqrt{32}}{\sqrt{- 50}}$

Step 1.4

Rewrite $- 50$ as $- 1 (50)$ .

$\frac{i \cdot \sqrt{32}}{\sqrt{- 1 (50)}}$

Step 1.5

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$\frac{i \cdot \sqrt{32}}{\sqrt{- 1} \cdot \sqrt{50}}$

Step 1.6

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

$\frac{i \cdot \sqrt{32}}{i \cdot \sqrt{50}}$

Step 2

Cancel the common factor of $i$ .

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Step 2.1

Cancel the common factor.

$\frac{i \cdot \sqrt{32}}{i \cdot \sqrt{50}}$

Step 2.2

Rewrite the expression.

$\frac{\sqrt{32}}{\sqrt{50}}$

Step 3

Combine $\sqrt{32}$ and $\sqrt{50}$ into a single radical.

$\sqrt{\frac{32}{50}}$

Step 4

Cancel the common factor of $32$ and $50$ .

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Step 4.1

Factor $2$ out of $32$ .

$\sqrt{\frac{2 (16)}{50}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $50$ .

$\sqrt{\frac{2 \cdot 16}{2 \cdot 25}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{2 \cdot 16}{2 \cdot 25}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{16}{25}}$

Step 5

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$\frac{\sqrt{16}}{\sqrt{25}}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2}}}{\sqrt{25}}$

Step 6.2

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

$\frac{4}{\sqrt{25}}$

Step 7

Simplify the denominator.

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Step 7.1

Rewrite $25$ as $5^{2}$ .

$\frac{4}{\sqrt{5^{2}}}$

Step 7.2

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

$\frac{4}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$