Simplify square root of 27x^5

$\sqrt{27 x^{5}}$

Step 1

Rewrite $27 x^{5}$ as ${(3 x^{2})}^{2} \cdot (3 x)$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) x^{5}}$

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

$\sqrt{3^{2} \cdot 3 x^{5}}$

Factor out $x^{4}$ .

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

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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