Simplify square root of 216x^4

$\sqrt{216 x^{4}}$

Step 1

Rewrite $216 x^{4}$ as ${(6 x^{2})}^{2} \cdot 6$ .

Factor $36$ out of $216$ .

$\sqrt{36 (6) x^{4}}$

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

$\sqrt{6^{2} \cdot 6 x^{4}}$

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

$\sqrt{6^{2} \cdot 6 {(x^{2})}^{2}}$

Move $6$ .

$\sqrt{6^{2} {(x^{2})}^{2} \cdot 6}$

Rewrite $6^{2} {(x^{2})}^{2}$ as ${(6 x^{2})}^{2}$ .

$\sqrt{{(6 x^{2})}^{2} \cdot 6}$

Step 2

Pull terms out from under the radical.

$6 x^{2} \sqrt{6}$