Solve frac{sqrt{2}frac{sqrt{3}}{2}}{sqrt{6}}

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

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

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

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

Express \frac{\frac{\sqrt{2}\sqrt{3}}{2}}{\sqrt{6}} as a single fraction.

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

Rationalize the denominator of \frac{\sqrt{2}\sqrt{3}}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

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

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

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

Multiply 2 and 6 to get 12.

$$\frac{6}{12}$$

Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$