Solve 1/sqrt{2}*1/5

$$\frac { 1 } { \sqrt { 2 } } \times \frac { 1 } { 5 }$$

Evaluate

$$\frac{\sqrt{2}}{10}\approx 0.141421356$$

Solution Steps

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

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{1}{5}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}\times \frac{1}{5}$$

Multiply \frac{\sqrt{2}}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{2}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{2}}{10}$$