Simplify square root of 108a^6

$\sqrt{108 a^{6}}$

Step 1

Rewrite $108 a^{6}$ as ${(6 a^{3})}^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$\sqrt{36 (3) a^{6}}$

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

$\sqrt{6^{2} \cdot 3 a^{6}}$

Rewrite $a^{6}$ as ${(a^{3})}^{2}$ .

$\sqrt{6^{2} \cdot 3 {(a^{3})}^{2}}$

Move $3$ .

$\sqrt{6^{2} {(a^{3})}^{2} \cdot 3}$

Rewrite $6^{2} {(a^{3})}^{2}$ as ${(6 a^{3})}^{2}$ .

$\sqrt{{(6 a^{3})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$6 a^{3} \sqrt{3}$