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Algebra Examples

$\sqrt{\frac{8 x}{9}}$

Step 1

Rewrite

$\frac{8 x}{9}$ as

${(\frac{2}{3})}^{2} (2 x)$ .

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Step 1.1

Factor the perfect power

$2^{2}$ out of

$8 x$ .

$\sqrt{\frac{2^{2} \cdot (2 x)}{9}}$

Step 1.2

Factor the perfect power

$3^{2}$ out of

$9$ .

$\sqrt{\frac{2^{2} \cdot (2 x)}{3^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction

$\frac{2^{2} \cdot (2 x)}{3^{2} \cdot 1}$ .

$\sqrt{{(\frac{2}{3})}^{2} (2 x)}$

$\sqrt{{(\frac{2}{3})}^{2} (2 x)}$

Step 2

Pull terms out from under the radical.

$\frac{2}{3} \sqrt{2 x}$

Step 3

Combine

$\frac{2}{3}$ and

$\sqrt{2 x}$ .

$\frac{2 \sqrt{2 x}}{3}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$