Simplify square root of 54x^3

$\sqrt{54 x^{3}}$

Step 1

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

Factor $9$ out of $54$ .

$\sqrt{9 (6) x^{3}}$

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

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

Factor out $x^{2}$ .

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

Move $6$ .

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

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

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

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

$3 x \sqrt{6 x}$

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