Solve (frac{sqrt{5}}{sqrt{6}}-frac{sqrt{2}}{sqrt{15}})

$$( \frac { \sqrt { 5 } } { \sqrt { 6 } } - \frac { \sqrt { 2 } } { \sqrt { 15 } } )$$

Evaluate

$$\frac{\sqrt{30}}{10}\approx 0.547722558$$

Solution Steps

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

$$\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}-\frac{\sqrt{2}}{\sqrt{15}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{5}\sqrt{6}}{6}-\frac{\sqrt{2}}{\sqrt{15}}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{6}-\frac{\sqrt{2}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{30}}{6}-\frac{\sqrt{2}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{30}}{6}-\frac{\sqrt{2}\sqrt{15}}{15}$$

To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{6}-\frac{\sqrt{30}}{15}$$

Combine \frac{\sqrt{30}}{6} and -\frac{\sqrt{30}}{15} to get \frac{1}{10}\sqrt{30}.

$$\frac{1}{10}\sqrt{30}$$