Simplify square root of 32a^9

$\sqrt{32 a^{9}}$

Step 1

Rewrite $32 a^{9}$ as ${(4 a^{4})}^{2} \cdot (2 a)$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2) a^{9}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 a^{9}}$

Factor out $a^{8}$ .

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

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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