Simplify square root of 54a^3b^2

$\sqrt{54 a^{3} b^{2}}$

Step 1

Rewrite $54 a^{3} b^{2}$ as ${(3 a b)}^{2} \cdot (6 a)$ .

Factor $9$ out of $54$ .

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

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

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

Factor out $a^{2}$ .

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

Move $a$ .

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

Move $6$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$3 a b \sqrt{6 a}$