Basic Math Examples

$- \sqrt{75} - \sqrt{12} - \sqrt{147}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $25$ out of $75$ .

$- \sqrt{25 (3)} - \sqrt{12} - \sqrt{147}$

Step 1.1.2

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

$- \sqrt{5^{2} \cdot 3} - \sqrt{12} - \sqrt{147}$

$- \sqrt{5^{2} \cdot 3} - \sqrt{12} - \sqrt{147}$

Step 1.2

Pull terms out from under the radical.

$- (5 \sqrt{3}) - \sqrt{12} - \sqrt{147}$

Step 1.3

Multiply $5$ by $- 1$ .

$- 5 \sqrt{3} - \sqrt{12} - \sqrt{147}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $12$ .

$- 5 \sqrt{3} - \sqrt{4 (3)} - \sqrt{147}$

Step 1.4.2

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

$- 5 \sqrt{3} - \sqrt{2^{2} \cdot 3} - \sqrt{147}$

$- 5 \sqrt{3} - \sqrt{2^{2} \cdot 3} - \sqrt{147}$

Step 1.5

Pull terms out from under the radical.

$- 5 \sqrt{3} - (2 \sqrt{3}) - \sqrt{147}$

Step 1.6

Multiply $2$ by $- 1$ .

$- 5 \sqrt{3} - 2 \sqrt{3} - \sqrt{147}$

Step 1.7

Rewrite $147$ as $7^{2} \cdot 3$ .

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Step 1.7.1

Factor $49$ out of $147$ .

$- 5 \sqrt{3} - 2 \sqrt{3} - \sqrt{49 (3)}$

Step 1.7.2

Rewrite $49$ as $7^{2}$ .

$- 5 \sqrt{3} - 2 \sqrt{3} - \sqrt{7^{2} \cdot 3}$

$- 5 \sqrt{3} - 2 \sqrt{3} - \sqrt{7^{2} \cdot 3}$

Step 1.8

Pull terms out from under the radical.

$- 5 \sqrt{3} - 2 \sqrt{3} - (7 \sqrt{3})$

Step 1.9

Multiply $7$ by $- 1$ .

$- 5 \sqrt{3} - 2 \sqrt{3} - 7 \sqrt{3}$

$- 5 \sqrt{3} - 2 \sqrt{3} - 7 \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 \sqrt{3}$ from $- 5 \sqrt{3}$ .

$- 7 \sqrt{3} - 7 \sqrt{3}$

Step 2.2

Subtract $7 \sqrt{3}$ from $- 7 \sqrt{3}$ .

$- 14 \sqrt{3}$

$- 14 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 14 \sqrt{3}$

Decimal Form:

$- 24.24871130 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$