Precalculus Examples

$\sqrt{\frac{25 y^{3}}{x^{2}}}$

Step 1

Rewrite $\frac{25 y^{3}}{x^{2}}$ as ${(\frac{5 y}{x})}^{2} y$ .

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Step 1.1

Factor the perfect power ${(5 y)}^{2}$ out of $25 y^{3}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Combine $\frac{5 y}{x}$ and $\sqrt{y}$ .

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