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Examples

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

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

Step 1

Rewrite

\frac{x}{4}

$\frac{x}{4}$ as

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

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

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Step 1.1

Factor the perfect power

1^{2}

$1^{2}$ out of

x

$x$ .

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

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

Step 1.2

Factor the perfect power

2^{2}

$2^{2}$ out of

4

$4$ .

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

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

Step 1.3

Rearrange the fraction

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

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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

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

Step 3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

\sqrt{x}

$\sqrt{x}$ .

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

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

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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