Simplify square root of 54x^7

$\sqrt{54 x^{7}}$

Step 1

Rewrite $54 x^{7}$ as ${(3 x^{3})}^{2} \cdot (6 x)$ .

Factor $9$ out of $54$ .

$\sqrt{9 (6) x^{7}}$

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

$\sqrt{3^{2} \cdot 6 x^{7}}$

Factor out $x^{6}$ .

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

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

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

Move $6$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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