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

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

Evaluate

$$\frac{\sqrt{3}}{2}\approx 0.866025404$$

Solution Steps

Divide \sqrt{3} by \sqrt{3} to get 1.

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

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

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

The square of \sqrt{3} is 3.

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

Cancel out 3 in both numerator and denominator.

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

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

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