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

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

Evaluate

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

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

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

The square of \sqrt{6} is 6.

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

Cancel out 2 in both numerator and denominator.

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