Solve left(frac{sqrt{3}}{3}+1/2right)frac{sqrt{3}}{2}

$$\left( \frac{ \sqrt{ 3 } }{ 3 } + \frac{ 1 }{ 2 } \right) \frac{ \sqrt{ 3 } }{ 2 }$$

Evaluate

$$\frac{\sqrt{3}+2}{4}\approx 0.933012702$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{\sqrt{3}}{3} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{3}{3}.

$$\left(\frac{2\sqrt{3}}{6}+\frac{3}{6}\right)\times \frac{\sqrt{3}}{2}$$

Since \frac{2\sqrt{3}}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

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

Multiply \frac{2\sqrt{3}+3}{6} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2\sqrt{3}+3\right)\sqrt{3}}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{\left(2\sqrt{3}+3\right)\sqrt{3}}{12}$$

Use the distributive property to multiply 2\sqrt{3}+3 by \sqrt{3}.

$$\frac{2\left(\sqrt{3}\right)^{2}+3\sqrt{3}}{12}$$

The square of \sqrt{3} is 3.

$$\frac{2\times 3+3\sqrt{3}}{12}$$

Multiply 2 and 3 to get 6.

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

Factor

$$\frac{\sqrt{3} + 2}{4} = 0.9330127018922193$$