Algebra Examples

$3 \sqrt{3} + 6 \sqrt{3} - \frac{1}{2} \sqrt{3}$

Step 1

Combine $\sqrt{3}$ and $\frac{1}{2}$ .

$3 \sqrt{3} + 6 \sqrt{3} - \frac{\sqrt{3}}{2}$

Step 2

Find the common denominator.

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Step 2.1

Write $3 \sqrt{3}$ as a fraction with denominator $1$ .

$\frac{3 \sqrt{3}}{1} + 6 \sqrt{3} - \frac{\sqrt{3}}{2}$

Step 2.2

Multiply $\frac{3 \sqrt{3}}{1}$ by $\frac{2}{2}$ .

$\frac{3 \sqrt{3}}{1} \cdot \frac{2}{2} + 6 \sqrt{3} - \frac{\sqrt{3}}{2}$

Step 2.3

Multiply $\frac{3 \sqrt{3}}{1}$ by $\frac{2}{2}$ .

$\frac{3 \sqrt{3} \cdot 2}{2} + 6 \sqrt{3} - \frac{\sqrt{3}}{2}$

Step 2.4

Write $6 \sqrt{3}$ as a fraction with denominator $1$ .

$\frac{3 \sqrt{3} \cdot 2}{2} + \frac{6 \sqrt{3}}{1} - \frac{\sqrt{3}}{2}$

Step 2.5

Multiply $\frac{6 \sqrt{3}}{1}$ by $\frac{2}{2}$ .

$\frac{3 \sqrt{3} \cdot 2}{2} + \frac{6 \sqrt{3}}{1} \cdot \frac{2}{2} - \frac{\sqrt{3}}{2}$

Step 2.6

Multiply $\frac{6 \sqrt{3}}{1}$ by $\frac{2}{2}$ .

$\frac{3 \sqrt{3} \cdot 2}{2} + \frac{6 \sqrt{3} \cdot 2}{2} - \frac{\sqrt{3}}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 \sqrt{3} \cdot 2 + 6 \sqrt{3} \cdot 2 - \sqrt{3}}{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply $2$ by $3$ .

$\frac{6 \sqrt{3} + 6 \sqrt{3} \cdot 2 - \sqrt{3}}{2}$

Step 4.2

Multiply $2$ by $6$ .

$\frac{6 \sqrt{3} + 12 \sqrt{3} - \sqrt{3}}{2}$

Step 5

Add $6 \sqrt{3}$ and $12 \sqrt{3}$ .

$\frac{18 \sqrt{3} - \sqrt{3}}{2}$

Step 6

Subtract $\sqrt{3}$ from $18 \sqrt{3}$ .

$\frac{17 \sqrt{3}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{17 \sqrt{3}}{2}$

Decimal Form:

$14.72243186 \dots$