Simplify square root of 8a^5

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

Step 1

Rewrite $8 a^{5}$ as ${(2 a^{2})}^{2} \cdot (2 a)$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2) a^{5}}$

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

$\sqrt{2^{2} \cdot 2 a^{5}}$

Factor out $a^{4}$ .

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

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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