Algebra Examples

$\sqrt{\frac{28}{x^{2}}} - \sqrt{\frac{7}{x^{2}}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\frac{28}{x^{2}}$ as ${(\frac{2}{x})}^{2} \cdot 7$ .

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Step 1.1.1

Factor the perfect power $2^{2}$ out of $28$ .

$\sqrt{\frac{2^{2} \cdot 7}{x^{2}}} - \sqrt{\frac{7}{x^{2}}}$

Step 1.1.2

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

$\sqrt{\frac{2^{2} \cdot 7}{x^{2} \cdot 1}} - \sqrt{\frac{7}{x^{2}}}$

Step 1.1.3

Rearrange the fraction $\frac{2^{2} \cdot 7}{x^{2} \cdot 1}$ .

$\sqrt{{(\frac{2}{x})}^{2} \cdot 7} - \sqrt{\frac{7}{x^{2}}}$

Step 1.2

Pull terms out from under the radical.

$\frac{2}{x} \sqrt{7} - \sqrt{\frac{7}{x^{2}}}$

Step 1.3

Combine $\frac{2}{x}$ and $\sqrt{7}$ .

$\frac{2 \sqrt{7}}{x} - \sqrt{\frac{7}{x^{2}}}$

Step 1.4

Rewrite $\frac{7}{x^{2}}$ as ${(\frac{1}{x})}^{2} \cdot 7$ .

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Step 1.4.1

Factor the perfect power $1^{2}$ out of $7$ .

$\frac{2 \sqrt{7}}{x} - \sqrt{\frac{1^{2} \cdot 7}{x^{2}}}$

Step 1.4.2

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

$\frac{2 \sqrt{7}}{x} - \sqrt{\frac{1^{2} \cdot 7}{x^{2} \cdot 1}}$

Step 1.4.3

Rearrange the fraction $\frac{1^{2} \cdot 7}{x^{2} \cdot 1}$ .

$\frac{2 \sqrt{7}}{x} - \sqrt{{(\frac{1}{x})}^{2} \cdot 7}$

Step 1.5

Pull terms out from under the radical.

$\frac{2 \sqrt{7}}{x} - (\frac{1}{x} \sqrt{7})$

Step 1.6

Combine $\frac{1}{x}$ and $\sqrt{7}$ .

$\frac{2 \sqrt{7}}{x} - \frac{\sqrt{7}}{x}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{2 \sqrt{7} - \sqrt{7}}{x}$

Step 2.2

Subtract $\sqrt{7}$ from $2 \sqrt{7}$ .

$\frac{\sqrt{7}}{x}$