Simplify 6 square root of 48x^2-2 square root of 27x^2- square root of 3x^2

$6 \sqrt{48 x^{2}} - 2 \sqrt{27 x^{2}} - \sqrt{3 x^{2}}$

Step 1

Simplify each term.

Rewrite $48 x^{2}$ as ${(4 x)}^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$6 \sqrt{16 (3) x^{2}} - 2 \sqrt{27 x^{2}} - \sqrt{3 x^{2}}$

Rewrite $16$ as $4^{2}$ .

$6 \sqrt{4^{2} \cdot 3 x^{2}} - 2 \sqrt{27 x^{2}} - \sqrt{3 x^{2}}$

Move $3$ .

$6 \sqrt{4^{2} x^{2} \cdot 3} - 2 \sqrt{27 x^{2}} - \sqrt{3 x^{2}}$

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

$6 \sqrt{{(4 x)}^{2} \cdot 3} - 2 \sqrt{27 x^{2}} - \sqrt{3 x^{2}}$

Pull terms out from under the radical.

$6 (4 x \sqrt{3}) - 2 \sqrt{27 x^{2}} - \sqrt{3 x^{2}}$

Multiply $4$ by $6$ .

$24 (x \sqrt{3}) - 2 \sqrt{27 x^{2}} - \sqrt{3 x^{2}}$

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

Factor $9$ out of $27$ .

$24 x \sqrt{3} - 2 \sqrt{9 (3) x^{2}} - \sqrt{3 x^{2}}$

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

$24 x \sqrt{3} - 2 \sqrt{3^{2} \cdot 3 x^{2}} - \sqrt{3 x^{2}}$

Move $3$ .

$24 x \sqrt{3} - 2 \sqrt{3^{2} x^{2} \cdot 3} - \sqrt{3 x^{2}}$

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

$24 x \sqrt{3} - 2 \sqrt{{(3 x)}^{2} \cdot 3} - \sqrt{3 x^{2}}$

Pull terms out from under the radical.

$24 x \sqrt{3} - 2 (3 x \sqrt{3}) - \sqrt{3 x^{2}}$

Multiply $3$ by $- 2$ .

$24 x \sqrt{3} - 6 (x \sqrt{3}) - \sqrt{3 x^{2}}$

Reorder $3$ and $x^{2}$ .

$24 x \sqrt{3} - 6 x \sqrt{3} - \sqrt{x^{2} \cdot 3}$

Pull terms out from under the radical.

$24 x \sqrt{3} - 6 x \sqrt{3} - x \sqrt{3}$

Step 2

Simplify by adding terms.

Subtract $6 x \sqrt{3}$ from $24 x \sqrt{3}$ .

$18 x \sqrt{3} - x \sqrt{3}$

Subtract $x \sqrt{3}$ from $18 x \sqrt{3}$ .

$17 x \sqrt{3}$