Simplify square root of 18a^5b^8

$\sqrt{18 a^{5} b^{8}}$

Step 1

Rewrite $18 a^{5} b^{8}$ as ${(3 a^{2} b^{4})}^{2} \cdot (2 a)$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2) a^{5} b^{8}}$

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

$\sqrt{3^{2} \cdot 2 a^{5} b^{8}}$

Factor out $a^{4}$ .

$\sqrt{3^{2} \cdot 2 (a^{4} a) b^{8}}$

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

$\sqrt{3^{2} \cdot 2 ({(a^{2})}^{2} a) b^{8}}$

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

$\sqrt{3^{2} \cdot 2 ({(a^{2})}^{2} a) {(b^{4})}^{2}}$

Move $a$ .

$\sqrt{3^{2} \cdot 2 ({(a^{2})}^{2}) {(b^{4})}^{2} a}$

Move $2$ .

$\sqrt{(3^{2} ({(a^{2})}^{2})) {(b^{4})}^{2} \cdot 2 a}$

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

$\sqrt{{(3 a^{2} b^{4})}^{2} \cdot 2 a}$

Add parentheses.

$\sqrt{{(3 a^{2} b^{4})}^{2} \cdot (2 a)}$

Step 2

Pull terms out from under the radical.

$3 a^{2} b^{4} \sqrt{2 a}$