Solve 5sqrt{2/5}

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

Evaluate

$$\sqrt{10}\approx 3.16227766$$

Solution Steps

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

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

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

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

The square of \sqrt{5} is 5.

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

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

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

Cancel out 5 and 5.

$$\sqrt{10}$$