Algebra Examples

$\frac{\sqrt{5 x}}{x \sqrt{20}}$

Step 1

Combine $\sqrt{5 x}$ and $\sqrt{20}$ into a single radical.

$\frac{\sqrt{\frac{5 x}{20}}}{x}$

Step 2

Cancel the common factor of $5$ and $20$ .

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Step 2.1

Factor $5$ out of $5 x$ .

$\frac{\sqrt{\frac{5 (x)}{20}}}{x}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $20$ .

$\frac{\sqrt{\frac{5 x}{5 \cdot 4}}}{x}$

Step 2.2.2

Cancel the common factor.

$\frac{\sqrt{\frac{5 x}{5 \cdot 4}}}{x}$

Step 2.2.3

Rewrite the expression.

$\frac{\sqrt{\frac{x}{4}}}{x}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $\frac{x}{4}$ as ${(\frac{1}{2})}^{2} x$ .

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Step 3.1.1

Factor the perfect power $1^{2}$ out of $x$ .

$\frac{\sqrt{\frac{1^{2} x}{4}}}{x}$

Step 3.1.2

Factor the perfect power $2^{2}$ out of $4$ .

$\frac{\sqrt{\frac{1^{2} x}{2^{2} \cdot 1}}}{x}$

Step 3.1.3

Rearrange the fraction $\frac{1^{2} x}{2^{2} \cdot 1}$ .

$\frac{\sqrt{{(\frac{1}{2})}^{2} x}}{x}$

Step 3.2

Pull terms out from under the radical.

$\frac{\frac{1}{2} \sqrt{x}}{x}$

Step 3.3

Combine $\frac{1}{2}$ and $\sqrt{x}$ .

$\frac{\frac{\sqrt{x}}{2}}{x}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{\sqrt{x}}{2} \cdot \frac{1}{x}$

Step 5

Multiply $\frac{\sqrt{x}}{2}$ by $\frac{1}{x}$ .

$\frac{\sqrt{x}}{2 x}$