Solve sqrt{5/2}/6

$$\sqrt { \frac { 5 } { 2 } } / 6$$

Evaluate

$$\frac{\sqrt{10}}{12}\approx 0.263523138$$

Solution Steps

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

$$\frac{\frac{\sqrt{5}}{\sqrt{2}}}{6}$$

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

$$\frac{\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{6}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{5}\sqrt{2}}{2}}{6}$$

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

$$\frac{\frac{\sqrt{10}}{2}}{6}$$

Express \frac{\frac{\sqrt{10}}{2}}{6} as a single fraction.

$$\frac{\sqrt{10}}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{\sqrt{10}}{12}$$