Simplify f(x) = square root of 216a^6b^8

$f (x) = \sqrt{216 a^{6} b^{8}}$

Rewrite $216 a^{6} b^{8}$ as ${(6 a^{3} b^{4})}^{2} \cdot 6$ .

Factor $36$ out of $216$ .

$f (x) = \sqrt{36 (6) a^{6} b^{8}}$

Rewrite $36$ as $6^{2}$ .

$f (x) = \sqrt{6^{2} \cdot (6 a^{6} b^{8})}$

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

$f (x) = \sqrt{6^{2} \cdot (6 {(a^{3})}^{2} b^{8})}$

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

$f (x) = \sqrt{6^{2} \cdot (6 {(a^{3})}^{2} {(b^{4})}^{2})}$

Move $6$ .

$f (x) = \sqrt{6^{2} {(a^{3})}^{2} {(b^{4})}^{2} \cdot 6}$

Rewrite $6^{2} {(a^{3})}^{2} {(b^{4})}^{2}$ as ${(6 a^{3} b^{4})}^{2}$ .

$f (x) = \sqrt{{(6 a^{3} b^{4})}^{2} \cdot 6}$

Pull terms out from under the radical.

$f (x) = 6 a^{3} b^{4} \sqrt{6}$