Simplify the Radical Expression square root of 81a^7b^12c^9

$\sqrt{81 a^{7} b^{12} c^{9}}$

Rewrite $81 a^{7} b^{12} c^{9}$ as ${(9 a^{3} b^{6} c^{4})}^{2} (a c)$ .

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} a^{7} b^{12} c^{9}}$

Factor out $a^{6}$ .

$\sqrt{9^{2} (a^{6} a) b^{12} c^{9}}$

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

$\sqrt{9^{2} ({(a^{3})}^{2} a) b^{12} c^{9}}$

Rewrite $b^{12}$ as ${(b^{6})}^{2}$ .

$\sqrt{9^{2} ({(a^{3})}^{2} a) {(b^{6})}^{2} c^{9}}$

Factor out $c^{8}$ .

$\sqrt{9^{2} ({(a^{3})}^{2} a) {(b^{6})}^{2} (c^{8} c)}$

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

$\sqrt{9^{2} ({(a^{3})}^{2} a) {(b^{6})}^{2} ({(c^{4})}^{2} c)}$

Move $a$ .

$\sqrt{9^{2} ({(a^{3})}^{2}) {(b^{6})}^{2} {(c^{4})}^{2} a c}$

Rewrite $9^{2} ({(a^{3})}^{2}) {(b^{6})}^{2} {(c^{4})}^{2}$ as ${(9 a^{3} b^{6} c^{4})}^{2}$ .

$\sqrt{{(9 a^{3} b^{6} c^{4})}^{2} a c}$

Add parentheses.

$\sqrt{{(9 a^{3} b^{6} c^{4})}^{2} (a c)}$

Pull terms out from under the radical.

$| 9 a^{3} b^{6} c^{4} | \sqrt{a c}$

Remove non-negative terms from the absolute value.

$9 b^{6} c^{4} | a^{3} | \sqrt{a c}$