Basic Math Examples

$\sqrt{3} - 7 \sqrt{48} + 7 \sqrt{12}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $16$ out of $48$ .

$\sqrt{3} - 7 \sqrt{16 (3)} + 7 \sqrt{12}$

Step 1.1.2

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

$\sqrt{3} - 7 \sqrt{4^{2} \cdot 3} + 7 \sqrt{12}$

$\sqrt{3} - 7 \sqrt{4^{2} \cdot 3} + 7 \sqrt{12}$

Step 1.2

Pull terms out from under the radical.

$\sqrt{3} - 7 (4 \sqrt{3}) + 7 \sqrt{12}$

Step 1.3

Multiply $4$ by $- 7$ .

$\sqrt{3} - 28 \sqrt{3} + 7 \sqrt{12}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $12$ .

$\sqrt{3} - 28 \sqrt{3} + 7 \sqrt{4 (3)}$

Step 1.4.2

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

$\sqrt{3} - 28 \sqrt{3} + 7 \sqrt{2^{2} \cdot 3}$

$\sqrt{3} - 28 \sqrt{3} + 7 \sqrt{2^{2} \cdot 3}$

Step 1.5

Pull terms out from under the radical.

$\sqrt{3} - 28 \sqrt{3} + 7 (2 \sqrt{3})$

Step 1.6

Multiply $2$ by $7$ .

$\sqrt{3} - 28 \sqrt{3} + 14 \sqrt{3}$

$\sqrt{3} - 28 \sqrt{3} + 14 \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $28 \sqrt{3}$ from $\sqrt{3}$ .

$- 27 \sqrt{3} + 14 \sqrt{3}$

Step 2.2

Add $- 27 \sqrt{3}$ and $14 \sqrt{3}$ .

$- 13 \sqrt{3}$

$- 13 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 13 \sqrt{3}$

Decimal Form:

$- 22.51666049 \dots$

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