Solve 4sqrt{2/5}

$$4 \sqrt { \frac { 2 } { 5 } }$$

Evaluate

$$\frac{4\sqrt{10}}{5}\approx 2.529822128$$

Solution Steps

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

$$4\times \frac{\sqrt{2}}{\sqrt{5}}$$

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

$$4\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$4\times \frac{\sqrt{2}\sqrt{5}}{5}$$

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

$$4\times \frac{\sqrt{10}}{5}$$

Express 4\times \frac{\sqrt{10}}{5} as a single fraction.

$$\frac{4\sqrt{10}}{5}$$