Solve frac{1/2sqrt{2}}{sqrt{3}}

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

Evaluate

$$\frac{\sqrt{6}}{6}\approx 0.40824829$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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