Basic Math Examples

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

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

Step 1

Simplify each term.

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Step 1.1

Rewrite

48

$48$ as

4^{2} \cdot 3

$4^{2} \cdot 3$ .

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Step 1.1.1

Factor

16

$16$ out of

48

$48$ .

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

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

Step 1.1.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

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

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

\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}

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

Step 1.3

Multiply

4

$4$ by

- 7

$- 7$ .

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

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

Step 1.4

Rewrite

12

$12$ as

2^{2} \cdot 3

$2^{2} \cdot 3$ .

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Step 1.4.1

Factor

4

$4$ out of

12

$12$ .

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

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

Step 1.4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

\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})

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

Step 1.6

Multiply

2

$2$ by

7

$7$ .

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

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

\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}

$28 \sqrt{3}$ from

\sqrt{3}

$\sqrt{3}$ .

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

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

Step 2.2

Add

- 27 \sqrt{3}

$- 27 \sqrt{3}$ and

14 \sqrt{3}

$14 \sqrt{3}$ .

- 13 \sqrt{3}

$- 13 \sqrt{3}$

- 13 \sqrt{3}

$- 13 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

- 13 \sqrt{3}

$- 13 \sqrt{3}$

Decimal Form:

- 22.51666049 \dots

$- 22.51666049 \dots$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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