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

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

Evaluate

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

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply \frac{\sqrt{3}}{3} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 3 and 2 to get 6.

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