Simplify 3 square root of 27x^3-2 square root of 12x^3

$3 \sqrt{27 x^{3}} - 2 \sqrt{12 x^{3}}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$3 \sqrt{9 (3) x^{3}} - 2 \sqrt{12 x^{3}}$

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

$3 \sqrt{3^{2} \cdot 3 x^{3}} - 2 \sqrt{12 x^{3}}$

Factor out $x^{2}$ .

$3 \sqrt{3^{2} \cdot 3 (x^{2} x)} - 2 \sqrt{12 x^{3}}$

Move $3$ .

$3 \sqrt{3^{2} x^{2} \cdot 3 x} - 2 \sqrt{12 x^{3}}$

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

$3 \sqrt{{(3 x)}^{2} \cdot 3 x} - 2 \sqrt{12 x^{3}}$

Add parentheses.

$3 \sqrt{{(3 x)}^{2} \cdot (3 x)} - 2 \sqrt{12 x^{3}}$

Pull terms out from under the radical.

$3 (3 x \sqrt{3 x}) - 2 \sqrt{12 x^{3}}$

Multiply $3$ by $3$ .

$9 (x \sqrt{3 x}) - 2 \sqrt{12 x^{3}}$

Rewrite $12 x^{3}$ as ${(2 x)}^{2} \cdot (3 x)$ .

Factor $4$ out of $12$ .

$9 x \sqrt{3 x} - 2 \sqrt{4 (3) x^{3}}$

Rewrite $4$ as $2^{2}$ .

$9 x \sqrt{3 x} - 2 \sqrt{2^{2} \cdot 3 x^{3}}$

Factor out $x^{2}$ .

$9 x \sqrt{3 x} - 2 \sqrt{2^{2} \cdot 3 (x^{2} x)}$

Move $3$ .

$9 x \sqrt{3 x} - 2 \sqrt{2^{2} x^{2} \cdot 3 x}$

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

$9 x \sqrt{3 x} - 2 \sqrt{{(2 x)}^{2} \cdot 3 x}$

Add parentheses.

$9 x \sqrt{3 x} - 2 \sqrt{{(2 x)}^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$9 x \sqrt{3 x} - 2 (2 x \sqrt{3 x})$

Multiply $2$ by $- 2$ .

$9 x \sqrt{3 x} - 4 x \sqrt{3 x}$

Step 2

Subtract $4 x \sqrt{3 x}$ from $9 x \sqrt{3 x}$ .

$5 x \sqrt{3 x}$