Solve 1/2*frac{sqrt{3}}{2}+2/sqrt{3}

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

Evaluate

$$\frac{11\sqrt{3}}{12}\approx 1.58771324$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\times 2 and 3 is 12. Multiply \frac{\sqrt{3}}{2\times 2} times \frac{3}{3}. Multiply \frac{2\sqrt{3}}{3} times \frac{4}{4}.

$$\frac{3\sqrt{3}}{12}+\frac{4\times 2\sqrt{3}}{12}$$

Since \frac{3\sqrt{3}}{12} and \frac{4\times 2\sqrt{3}}{12} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{3}+4\times 2\sqrt{3}}{12}$$

Do the multiplications in 3\sqrt{3}+4\times 2\sqrt{3}.

$$\frac{3\sqrt{3}+8\sqrt{3}}{12}$$

Do the calculations in 3\sqrt{3}+8\sqrt{3}.

$$\frac{11\sqrt{3}}{12}$$