Pre-Algebra Examples

$\frac{2}{7} \sqrt{108} + 6 \sqrt{12}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $108$ as $6^{2} \cdot 3$ .

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Step 1.1.1

Factor $36$ out of $108$ .

$\frac{2}{7} \cdot \sqrt{36 (3)} + 6 \sqrt{12}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

$\frac{2}{7} \cdot \sqrt{6^{2} \cdot 3} + 6 \sqrt{12}$

Step 1.2

Pull terms out from under the radical.

$\frac{2}{7} \cdot (6 \sqrt{3}) + 6 \sqrt{12}$

Step 1.3

Multiply $\frac{2}{7} (6 \sqrt{3})$ .

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Step 1.3.1

Combine $6$ and $\frac{2}{7}$ .

$\frac{6 \cdot 2}{7} \sqrt{3} + 6 \sqrt{12}$

Step 1.3.2

Multiply $6$ by $2$ .

$\frac{12}{7} \sqrt{3} + 6 \sqrt{12}$

Step 1.3.3

Combine $\frac{12}{7}$ and $\sqrt{3}$ .

$\frac{12 \sqrt{3}}{7} + 6 \sqrt{12}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $12$ .

$\frac{12 \sqrt{3}}{7} + 6 \sqrt{4 (3)}$

Step 1.4.2

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

$\frac{12 \sqrt{3}}{7} + 6 \sqrt{2^{2} \cdot 3}$

Step 1.5

Pull terms out from under the radical.

$\frac{12 \sqrt{3}}{7} + 6 (2 \sqrt{3})$

Step 1.6

Multiply $2$ by $6$ .

$\frac{12 \sqrt{3}}{7} + 12 \sqrt{3}$

Step 2

To write $12 \sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{12 \sqrt{3}}{7} + 12 \sqrt{3} \cdot \frac{7}{7}$

Step 3

Combine fractions.

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Step 3.1

Combine $12 \sqrt{3}$ and $\frac{7}{7}$ .

$\frac{12 \sqrt{3}}{7} + \frac{12 \sqrt{3} \cdot 7}{7}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{12 \sqrt{3} + 12 \sqrt{3} \cdot 7}{7}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $7$ by $12$ .

$\frac{12 \sqrt{3} + 84 \sqrt{3}}{7}$

Step 4.2

Add $12 \sqrt{3}$ and $84 \sqrt{3}$ .

$\frac{96 \sqrt{3}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{96 \sqrt{3}}{7}$

Decimal Form:

$23.75383964 \dots$