Simplify square root of 162c^4d^6

$\sqrt{162 c^{4} d^{6}}$

Step 1

Rewrite $162 c^{4} d^{6}$ as ${(9 c^{2} d^{3})}^{2} \cdot 2$ .

Factor $81$ out of $162$ .

$\sqrt{81 (2) c^{4} d^{6}}$

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

$\sqrt{9^{2} \cdot 2 c^{4} d^{6}}$

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

$\sqrt{9^{2} \cdot 2 {(c^{2})}^{2} d^{6}}$

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

$\sqrt{9^{2} \cdot 2 {(c^{2})}^{2} {(d^{3})}^{2}}$

Move $2$ .

$\sqrt{9^{2} {(c^{2})}^{2} {(d^{3})}^{2} \cdot 2}$

Rewrite $9^{2} {(c^{2})}^{2} {(d^{3})}^{2}$ as ${(9 c^{2} d^{3})}^{2}$ .

$\sqrt{{(9 c^{2} d^{3})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$9 c^{2} d^{3} \sqrt{2}$