Precalculus Examples

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

Step 1

Rewrite $\frac{5 x}{4}$ as ${(\frac{1}{2})}^{2} (5 x)$ .

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Step 1.1

Factor the perfect power $1^{2}$ out of $5 x$ .

$\sqrt{\frac{1^{2} (5 x)}{4}}$

Step 1.2

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

$\sqrt{\frac{1^{2} (5 x)}{2^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{1^{2} (5 x)}{2^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{2})}^{2} (5 x)}$

Step 2

Pull terms out from under the radical.

$\frac{1}{2} \sqrt{5 x}$

Step 3

Combine $\frac{1}{2}$ and $\sqrt{5 x}$ .

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