Simplify square root of 12r^9s^12

$\sqrt{12 r^{9} s^{12}}$

Step 1

Rewrite $12 r^{9} s^{12}$ as ${(2 r^{4} s^{6})}^{2} \cdot (3 r)$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3) r^{9} s^{12}}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 3 r^{9} s^{12}}$

Factor out $r^{8}$ .

$\sqrt{2^{2} \cdot 3 (r^{8} r) s^{12}}$

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

$\sqrt{2^{2} \cdot 3 ({(r^{4})}^{2} r) s^{12}}$

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

$\sqrt{2^{2} \cdot 3 ({(r^{4})}^{2} r) {(s^{6})}^{2}}$

Move $r$ .

$\sqrt{2^{2} \cdot 3 ({(r^{4})}^{2}) {(s^{6})}^{2} r}$

Move $3$ .

$\sqrt{(2^{2} ({(r^{4})}^{2})) {(s^{6})}^{2} \cdot 3 r}$

Rewrite $(2^{2} ({(r^{4})}^{2})) {(s^{6})}^{2}$ as ${(2 r^{4} s^{6})}^{2}$ .

$\sqrt{{(2 r^{4} s^{6})}^{2} \cdot 3 r}$

Add parentheses.

$\sqrt{{(2 r^{4} s^{6})}^{2} \cdot (3 r)}$

Step 2

Pull terms out from under the radical.

$2 r^{4} s^{6} \sqrt{3 r}$