Basic Math Examples

$3 \sqrt{3} + 2 \sqrt{12} + \sqrt{12} + 4 \sqrt{75}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $12$ .

$3 \sqrt{3} + 2 \sqrt{4 (3)} + \sqrt{12} + 4 \sqrt{75}$

Step 1.1.2

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

$3 \sqrt{3} + 2 \sqrt{2^{2} \cdot 3} + \sqrt{12} + 4 \sqrt{75}$

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{3} + 2 (2 \sqrt{3}) + \sqrt{12} + 4 \sqrt{75}$

Step 1.3

Multiply $2$ by $2$ .

$3 \sqrt{3} + 4 \sqrt{3} + \sqrt{12} + 4 \sqrt{75}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $12$ .

$3 \sqrt{3} + 4 \sqrt{3} + \sqrt{4 (3)} + 4 \sqrt{75}$

Step 1.4.2

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

$3 \sqrt{3} + 4 \sqrt{3} + \sqrt{2^{2} \cdot 3} + 4 \sqrt{75}$

Step 1.5

Pull terms out from under the radical.

$3 \sqrt{3} + 4 \sqrt{3} + 2 \sqrt{3} + 4 \sqrt{75}$

Step 1.6

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

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Step 1.6.1

Factor $25$ out of $75$ .

$3 \sqrt{3} + 4 \sqrt{3} + 2 \sqrt{3} + 4 \sqrt{25 (3)}$

Step 1.6.2

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

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

Step 1.7

Pull terms out from under the radical.

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

Step 1.8

Multiply $5$ by $4$ .

$3 \sqrt{3} + 4 \sqrt{3} + 2 \sqrt{3} + 20 \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $3 \sqrt{3}$ and $4 \sqrt{3}$ .

$7 \sqrt{3} + 2 \sqrt{3} + 20 \sqrt{3}$

Step 2.2

Add $7 \sqrt{3}$ and $2 \sqrt{3}$ .

$9 \sqrt{3} + 20 \sqrt{3}$

Step 2.3

Add $9 \sqrt{3}$ and $20 \sqrt{3}$ .

$29 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$29 \sqrt{3}$

Decimal Form:

$50.22947341 \dots$