Simplify square root of 8a^3b^8

$\sqrt{8 a^{3} b^{8}}$

Step 1

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

Factor $4$ out of $8$ .

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

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

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

Factor out $a^{2}$ .

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

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

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

Move $a$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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