Simplify square root of 27x^7

$\sqrt{27 x^{7}}$

Step 1

Rewrite $27 x^{7}$ as ${(3 x^{3})}^{2} \cdot (3 x)$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) x^{7}}$

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

$\sqrt{3^{2} \cdot 3 x^{7}}$

Factor out $x^{6}$ .

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

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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