Simplify square root of 27x^3

$\sqrt{27 x^{3}}$

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

Factor $9$ out of $27$ .

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

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

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

Factor out $x^{2}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

$3 x \sqrt{3 x}$

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