Finite Math Examples

$\sqrt{\frac{101 x^{14}}{25 y^{8}}}$

Step 1

Rewrite $\frac{101 x^{14}}{25 y^{8}}$ as ${(\frac{x^{7}}{5 y^{4}})}^{2} \cdot 101$ .

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Step 1.1

Factor the perfect power ${(x^{7})}^{2}$ out of $101 x^{14}$ .

$\sqrt{\frac{{(x^{7})}^{2} \cdot 101}{25 y^{8}}}$

Step 1.2

Factor the perfect power ${(5 y^{4})}^{2}$ out of $25 y^{8}$ .

$\sqrt{\frac{{(x^{7})}^{2} \cdot 101}{{(5 y^{4})}^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{{(x^{7})}^{2} \cdot 101}{{(5 y^{4})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{x^{7}}{5 y^{4}})}^{2} \cdot 101}$

Step 2

Pull terms out from under the radical.

$\frac{x^{7}}{5 y^{4}} \sqrt{101}$

Step 3

Combine $\frac{x^{7}}{5 y^{4}}$ and $\sqrt{101}$ .

$\frac{x^{7} \sqrt{101}}{5 y^{4}}$