Solve 1/2(sqrt{2/sqrt{3})}

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

Evaluate

$$\frac{\sqrt{6}}{4}\approx 0.612372436$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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

Divide 1 by \frac{2\sqrt{6}}{3} by multiplying 1 by the reciprocal of \frac{2\sqrt{6}}{3}.

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

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

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

The square of \sqrt{6} is 6.

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

Cancel out 3 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{6}}{4}$$