Algebra Examples

$\frac{2 \sqrt{12}}{\sqrt{75}}$

Step 1

Combine $\sqrt{12}$ and $\sqrt{75}$ into a single radical.

$2 \sqrt{\frac{12}{75}}$

Step 2

Cancel the common factor of $12$ and $75$ .

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Step 2.1

Factor $3$ out of $12$ .

$2 \sqrt{\frac{3 (4)}{75}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $75$ .

$2 \sqrt{\frac{3 \cdot 4}{3 \cdot 25}}$

Step 2.2.2

Cancel the common factor.

$2 \sqrt{\frac{3 \cdot 4}{3 \cdot 25}}$

Step 2.2.3

Rewrite the expression.

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

Step 3

Rewrite $\sqrt{\frac{4}{25}}$ as $\frac{\sqrt{4}}{\sqrt{25}}$ .

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

Step 4

Simplify the numerator.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Simplify the denominator.

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Step 5.1

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

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

Step 5.2

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

$2 (\frac{2}{5})$

Step 6

Multiply $2 (\frac{2}{5})$ .

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Step 6.1

Combine $2$ and $\frac{2}{5}$ .

$\frac{2 \cdot 2}{5}$

Step 6.2

Multiply $2$ by $2$ .

$\frac{4}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$