Simplify square root of 27x^4

$\sqrt{27 x^{4}}$

Step 1

Rewrite $27 x^{4}$ as ${(3 x^{2})}^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) x^{4}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 3 x^{4}}$

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

$\sqrt{3^{2} \cdot 3 {(x^{2})}^{2}}$

Move $3$ .

$\sqrt{3^{2} {(x^{2})}^{2} \cdot 3}$

Rewrite $3^{2} {(x^{2})}^{2}$ as ${(3 x^{2})}^{2}$ .

$\sqrt{{(3 x^{2})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$3 x^{2} \sqrt{3}$