Solve 2sqrt{3}-1/2sqrt{3}

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

Evaluate

$$\frac{11\sqrt{3}}{6}\approx 3.175426481$$

Solution Steps

Rationalize the denominator of \frac{1}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

Combine 2\sqrt{3} and -\frac{\sqrt{3}}{6} to get \frac{11}{6}\sqrt{3}.

$$\frac{11}{6}\sqrt{3}$$