Solve sqrt{5/2}-sqrt{2/5}

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

Evaluate

$$\frac{3\sqrt{10}}{10}\approx 0.948683298$$

Short Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

$$\frac{\sqrt{10}}{2}-\frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 5 is 10. Multiply \frac{\sqrt{10}}{2} times \frac{5}{5}. Multiply \frac{\sqrt{10}}{5} times \frac{2}{2}.

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

Since \frac{5\sqrt{10}}{10} and \frac{2\sqrt{10}}{10} have the same denominator, subtract them by subtracting their numerators.

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

Do the calculations in 5\sqrt{10}-2\sqrt{10}.

$$\frac{3\sqrt{10}}{10}$$