Solve 1/2sqrt{2/5}

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

Evaluate

$$\frac{\sqrt{10}}{10}\approx 0.316227766$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

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

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{1}{2}\times \frac{\sqrt{10}}{5}$$

Multiply \frac{1}{2} times \frac{\sqrt{10}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{10}}{2\times 5}$$

Multiply 2 and 5 to get 10.

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