Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $12$ .

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

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $2$ by $5$ .

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

Step 1.4

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

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Step 1.4.1

Factor $25$ out of $75$ .

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

Step 1.4.2

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

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Multiply $5$ by $- 6$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

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

$- 13 x \sqrt{3}$