Basic Math Examples

5 \sqrt{3} - \sqrt{27} + 2 \sqrt{48}

$5 \sqrt{3} - \sqrt{27} + 2 \sqrt{48}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

27

$27$ as

3^{2} \cdot 3

$3^{2} \cdot 3$ .

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Step 1.1.1

Factor

9

$9$ out of

27

$27$ .

5 \sqrt{3} - \sqrt{9 (3)} + 2 \sqrt{48}

$5 \sqrt{3} - \sqrt{9 (3)} + 2 \sqrt{48}$

Step 1.1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

5 \sqrt{3} - \sqrt{3^{2} \cdot 3} + 2 \sqrt{48}

$5 \sqrt{3} - \sqrt{3^{2} \cdot 3} + 2 \sqrt{48}$

5 \sqrt{3} - \sqrt{3^{2} \cdot 3} + 2 \sqrt{48}

$5 \sqrt{3} - \sqrt{3^{2} \cdot 3} + 2 \sqrt{48}$

Step 1.2

Pull terms out from under the radical.

5 \sqrt{3} - (3 \sqrt{3}) + 2 \sqrt{48}

$5 \sqrt{3} - (3 \sqrt{3}) + 2 \sqrt{48}$

Step 1.3

Multiply

3

$3$ by

- 1

$- 1$ .

5 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{48}

$5 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{48}$

Step 1.4

Rewrite

48

$48$ as

4^{2} \cdot 3

$4^{2} \cdot 3$ .

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Step 1.4.1

Factor

16

$16$ out of

48

$48$ .

5 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{16 (3)}

$5 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{16 (3)}$

Step 1.4.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

5 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{4^{2} \cdot 3}

$5 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{4^{2} \cdot 3}$

5 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{4^{2} \cdot 3}

$5 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{4^{2} \cdot 3}$

Step 1.5

Pull terms out from under the radical.

5 \sqrt{3} - 3 \sqrt{3} + 2 (4 \sqrt{3})

$5 \sqrt{3} - 3 \sqrt{3} + 2 (4 \sqrt{3})$

Step 1.6

Multiply

4

$4$ by

2

$2$ .

5 \sqrt{3} - 3 \sqrt{3} + 8 \sqrt{3}

$5 \sqrt{3} - 3 \sqrt{3} + 8 \sqrt{3}$

5 \sqrt{3} - 3 \sqrt{3} + 8 \sqrt{3}

$5 \sqrt{3} - 3 \sqrt{3} + 8 \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract

3 \sqrt{3}

$3 \sqrt{3}$ from

5 \sqrt{3}

$5 \sqrt{3}$ .

2 \sqrt{3} + 8 \sqrt{3}

$2 \sqrt{3} + 8 \sqrt{3}$

Step 2.2

Add

2 \sqrt{3}

$2 \sqrt{3}$ and

8 \sqrt{3}

$8 \sqrt{3}$ .

10 \sqrt{3}

$10 \sqrt{3}$

10 \sqrt{3}

$10 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

10 \sqrt{3}

$10 \sqrt{3}$

Decimal Form:

17.32050807 \dots

$17.32050807 \dots$

5 \sqrt[]{3} - \sqrt[]{27} + 2 \sqrt[]{48}

$5 \sqrt[]{3} - \sqrt[]{27} + 2 \sqrt[]{48}$

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

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