Pre-Algebra Examples

$\sqrt{\frac{x^{11}}{36}}$

Step 1

Rewrite $\frac{x^{11}}{36}$ as ${(\frac{x^{5}}{6})}^{2} x$ .

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Step 1.1

Factor the perfect power ${(x^{5})}^{2}$ out of $x^{11}$ .

$\sqrt{\frac{{(x^{5})}^{2} x}{36}}$

Step 1.2

Factor the perfect power $6^{2}$ out of $36$ .

$\sqrt{\frac{{(x^{5})}^{2} x}{6^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{{(x^{5})}^{2} x}{6^{2} \cdot 1}$ .

$\sqrt{{(\frac{x^{5}}{6})}^{2} x}$

Step 2

Pull terms out from under the radical.

$\frac{x^{5}}{6} \sqrt{x}$

Step 3

Combine $\frac{x^{5}}{6}$ and $\sqrt{x}$ .

$\frac{x^{5} \sqrt{x}}{6}$