Simplify square root of 72a^15

$\sqrt{72 a^{15}}$

Step 1

Rewrite $72 a^{15}$ as ${(6 a^{7})}^{2} \cdot (2 a)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) a^{15}}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2 a^{15}}$

Factor out $a^{14}$ .

$\sqrt{6^{2} \cdot 2 (a^{14} a)}$

Rewrite $a^{14}$ as ${(a^{7})}^{2}$ .

$\sqrt{6^{2} \cdot 2 ({(a^{7})}^{2} a)}$

Move $2$ .

$\sqrt{6^{2} {(a^{7})}^{2} \cdot 2 a}$

Rewrite $6^{2} {(a^{7})}^{2}$ as ${(6 a^{7})}^{2}$ .

$\sqrt{{(6 a^{7})}^{2} \cdot 2 a}$

Add parentheses.

$\sqrt{{(6 a^{7})}^{2} \cdot (2 a)}$

Step 2

Pull terms out from under the radical.

$6 a^{7} \sqrt{2 a}$