Solve 3/2/3sqrt{3}

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

Evaluate

$$\frac{\sqrt{3}}{6}\approx 0.288675135$$

Solution Steps

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

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

Multiply 2 and 3 to get 6.

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

Rationalize the denominator of \frac{3}{6\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Cancel out 3 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

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