Solve frac{sqrt{5}}{6sqrt{2}}

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

Evaluate

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

Solution Steps

Rationalize the denominator of \frac{\sqrt{5}}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 6 and 2 to get 12.

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