Basic Math Examples

\sqrt{75} + 2 \sqrt{108} - 3 \sqrt{3}

$\sqrt{75} + 2 \sqrt{108} - 3 \sqrt{3}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

75

$75$ as

5^{2} \cdot 3

$5^{2} \cdot 3$ .

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Step 1.1.1

Factor

25

$25$ out of

75

$75$ .

\sqrt{25 (3)} + 2 \sqrt{108} - 3 \sqrt{3}

$\sqrt{25 (3)} + 2 \sqrt{108} - 3 \sqrt{3}$

Step 1.1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\sqrt{5^{2} \cdot 3} + 2 \sqrt{108} - 3 \sqrt{3}

$\sqrt{5^{2} \cdot 3} + 2 \sqrt{108} - 3 \sqrt{3}$

\sqrt{5^{2} \cdot 3} + 2 \sqrt{108} - 3 \sqrt{3}

$\sqrt{5^{2} \cdot 3} + 2 \sqrt{108} - 3 \sqrt{3}$

Step 1.2

Pull terms out from under the radical.

5 \sqrt{3} + 2 \sqrt{108} - 3 \sqrt{3}

$5 \sqrt{3} + 2 \sqrt{108} - 3 \sqrt{3}$

Step 1.3

Rewrite

108

$108$ as

6^{2} \cdot 3

$6^{2} \cdot 3$ .

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Step 1.3.1

Factor

36

$36$ out of

108

$108$ .

5 \sqrt{3} + 2 \sqrt{36 (3)} - 3 \sqrt{3}

$5 \sqrt{3} + 2 \sqrt{36 (3)} - 3 \sqrt{3}$

Step 1.3.2

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

5 \sqrt{3} + 2 \sqrt{6^{2} \cdot 3} - 3 \sqrt{3}

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

5 \sqrt{3} + 2 \sqrt{6^{2} \cdot 3} - 3 \sqrt{3}

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

Step 1.4

Pull terms out from under the radical.

5 \sqrt{3} + 2 (6 \sqrt{3}) - 3 \sqrt{3}

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

Step 1.5

Multiply

6

$6$ by

2

$2$ .

5 \sqrt{3} + 12 \sqrt{3} - 3 \sqrt{3}

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

5 \sqrt{3} + 12 \sqrt{3} - 3 \sqrt{3}

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

Step 2

Simplify by adding terms.

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Step 2.1

Add

5 \sqrt{3}

$5 \sqrt{3}$ and

12 \sqrt{3}

$12 \sqrt{3}$ .

17 \sqrt{3} - 3 \sqrt{3}

$17 \sqrt{3} - 3 \sqrt{3}$

Step 2.2

Subtract

3 \sqrt{3}

$3 \sqrt{3}$ from

17 \sqrt{3}

$17 \sqrt{3}$ .

14 \sqrt{3}

$14 \sqrt{3}$

14 \sqrt{3}

$14 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

14 \sqrt{3}

$14 \sqrt{3}$

Decimal Form:

24.24871130 \dots

$24.24871130 \dots$