Simplify square root of (a^4b^3)/(16c^4)

$\sqrt{\frac{a^{4} b^{3}}{16 c^{4}}}$

Step 1

Rewrite $\frac{a^{4} b^{3}}{16 c^{4}}$ as ${(\frac{a^{2} b}{4 c^{2}})}^{2} b$ .

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

$\sqrt{\frac{{(a^{2} b)}^{2} b}{16 c^{4}}}$

Factor the perfect power ${(4 c^{2})}^{2}$ out of $16 c^{4}$ .

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

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

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

Step 2

Pull terms out from under the radical.

$\frac{a^{2} b}{4 c^{2}} \sqrt{b}$

Step 3

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

$\frac{a^{2} b \sqrt{b}}{4 c^{2}}$