Simplify 5x square root of 12-6x square root of 75+7x square root of 3

$5 x \sqrt{12} - 6 x \sqrt{75} + 7 x \sqrt{3}$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

$5 x \sqrt{4 (3)} - 6 x \sqrt{75} + 7 x \sqrt{3}$

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

$5 x \sqrt{2^{2} \cdot 3} - 6 x \sqrt{75} + 7 x \sqrt{3}$

Pull terms out from under the radical.

$5 x (2 \sqrt{3}) - 6 x \sqrt{75} + 7 x \sqrt{3}$

Multiply $2$ by $5$ .

$10 x \sqrt{3} - 6 x \sqrt{75} + 7 x \sqrt{3}$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$10 x \sqrt{3} - 6 x \sqrt{25 (3)} + 7 x \sqrt{3}$

Rewrite $25$ as $5^{2}$ .

$10 x \sqrt{3} - 6 x \sqrt{5^{2} \cdot 3} + 7 x \sqrt{3}$

Pull terms out from under the radical.

$10 x \sqrt{3} - 6 x (5 \sqrt{3}) + 7 x \sqrt{3}$

Multiply $5$ by $- 6$ .

$10 x \sqrt{3} - 30 x \sqrt{3} + 7 x \sqrt{3}$

Step 2

Simplify by adding terms.

Subtract $30 x \sqrt{3}$ from $10 x \sqrt{3}$ .

$- 20 x \sqrt{3} + 7 x \sqrt{3}$

Add $- 20 x \sqrt{3}$ and $7 x \sqrt{3}$ .

$- 13 x \sqrt{3}$