Solve sqrt{1/2}*1/10

$$\sqrt { \frac { 1 } { 2 } } \cdot \frac { 1 } { 10 }$$

Evaluate

$$\frac{\sqrt{2}}{20}\approx 0.070710678$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{\sqrt{1}}{\sqrt{2}}\times \frac{1}{10}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{2}}\times \frac{1}{10}$$

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

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{1}{10}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}\times \frac{1}{10}$$

Multiply \frac{\sqrt{2}}{2} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 10 to get 20.

$$\frac{\sqrt{2}}{20}$$