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

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

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

Multiply 2 and 3 to get 6.

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

Divide 3\sqrt{6} by 6 to get \frac{1}{2}\sqrt{6}.

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