Solve 1/2sqrt{3}-1/6

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

Evaluate

$$\frac{\sqrt{3}-1}{6}\approx 0.122008468$$

Solution Steps

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

$$\frac{\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}-\frac{1}{6}$$

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

Since \frac{\sqrt{3}}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

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

Factor

$$\frac{\sqrt{3} - 1}{6} = 0.1220084679281462$$