Simplify square root of 72x^4

$\sqrt{72 x^{4}}$

Step 1

Rewrite $72 x^{4}$ as ${(6 x^{2})}^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) x^{4}}$

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

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

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

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

Move $2$ .

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

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

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

Step 2

Pull terms out from under the radical.

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