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

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

Evaluate

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

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 2 and 2 to get 4.

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