Pre-Algebra Examples

$\sqrt{\frac{20 a^{5}}{9 b^{8}}}$

Step 1

Rewrite $\frac{20 a^{5}}{9 b^{8}}$ as ${(\frac{2 a^{2}}{3 b^{4}})}^{2} (5 a)$ .

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Step 1.1

Factor the perfect power ${(2 a^{2})}^{2}$ out of $20 a^{5}$ .

$\sqrt{\frac{{(2 a^{2})}^{2} \cdot (5 a)}{9 b^{8}}}$

Step 1.2

Factor the perfect power ${(3 b^{4})}^{2}$ out of $9 b^{8}$ .

$\sqrt{\frac{{(2 a^{2})}^{2} \cdot (5 a)}{{(3 b^{4})}^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{{(2 a^{2})}^{2} \cdot (5 a)}{{(3 b^{4})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{2 a^{2}}{3 b^{4}})}^{2} (5 a)}$

Step 2

Pull terms out from under the radical.

$\frac{2 a^{2}}{3 b^{4}} \sqrt{5 a}$

Step 3

Combine $\frac{2 a^{2}}{3 b^{4}}$ and $\sqrt{5 a}$ .

$\frac{2 a^{2} \sqrt{5 a}}{3 b^{4}}$