Simplify square root of (a^8b^2)/(c^6)

$\sqrt{\frac{a^{8} b^{2}}{c^{6}}}$

Step 1

Rewrite $a^{8} b^{2}$ as ${(a^{4} b)}^{2}$ .

$\sqrt{\frac{{(a^{4} b)}^{2}}{c^{6}}}$

Step 2

Rewrite $c^{6}$ as ${(c^{3})}^{2}$ .

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

Step 3

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

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

Step 4

Pull terms out from under the radical, assuming positive real numbers.

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