Simplify square root of 72a^19

$\sqrt{72 a^{19}}$

Step 1

Rewrite $72 a^{19}$ as ${(6 a^{9})}^{2} \cdot (2 a)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) a^{19}}$

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

$\sqrt{6^{2} \cdot 2 a^{19}}$

Factor out $a^{18}$ .

$\sqrt{6^{2} \cdot 2 (a^{18} a)}$

Rewrite $a^{18}$ as ${(a^{9})}^{2}$ .

$\sqrt{6^{2} \cdot 2 ({(a^{9})}^{2} a)}$

Move $2$ .

$\sqrt{6^{2} {(a^{9})}^{2} \cdot 2 a}$

Rewrite $6^{2} {(a^{9})}^{2}$ as ${(6 a^{9})}^{2}$ .

$\sqrt{{(6 a^{9})}^{2} \cdot 2 a}$

Add parentheses.

$\sqrt{{(6 a^{9})}^{2} \cdot (2 a)}$

Step 2

Pull terms out from under the radical.

$6 a^{9} \sqrt{2 a}$