Solve frac{sqrt{3}}{2}quad1/2/sqrt{3}

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

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Express \frac{\frac{1}{2}}{\sqrt{3}} as a single fraction.

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

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

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

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

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 2 and 6 to get 12.

$$\frac{3}{12}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$