Simplify square root of (9a^5)/(64b^4)

$\sqrt{\frac{9 a^{5}}{64 b^{4}}}$

Step 1

Rewrite $\frac{9 a^{5}}{64 b^{4}}$ as ${(\frac{3 a^{2}}{8 b^{2}})}^{2} a$ .

Factor the perfect power ${(3 a^{2})}^{2}$ out of $9 a^{5}$ .

$\sqrt{\frac{{(3 a^{2})}^{2} a}{64 b^{4}}}$

Factor the perfect power ${(8 b^{2})}^{2}$ out of $64 b^{4}$ .

$\sqrt{\frac{{(3 a^{2})}^{2} a}{{(8 b^{2})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(3 a^{2})}^{2} a}{{(8 b^{2})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{3 a^{2}}{8 b^{2}})}^{2} a}$

Step 2

Pull terms out from under the radical.

$\frac{3 a^{2}}{8 b^{2}} \sqrt{a}$

Step 3

Combine $\frac{3 a^{2}}{8 b^{2}}$ and $\sqrt{a}$ .

$\frac{3 a^{2} \sqrt{a}}{8 b^{2}}$