Simplify square root of 18a^6b^2

$\sqrt{18 a^{6} b^{2}}$

Step 1

Rewrite $18 a^{6} b^{2}$ as ${(3 a^{3} b)}^{2} \cdot 2$ .

Factor $9$ out of $18$ .

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

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 a^{6} b^{2}}$

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

$\sqrt{3^{2} \cdot 2 {(a^{3})}^{2} b^{2}}$

Move $2$ .

$\sqrt{3^{2} {(a^{3})}^{2} b^{2} \cdot 2}$

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

$\sqrt{{(3 a^{3} b)}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$3 a^{3} b \sqrt{2}$