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

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

Evaluate

$$\frac{3}{10}=0.3$$

Solution Steps

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

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

The square of \sqrt{6} is 6.

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

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

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

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

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

The square of \sqrt{15} is 15.

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

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

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

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

$$\left(\frac{1}{10}\sqrt{30}\right)^{2}$$

Expand \left(\frac{1}{10}\sqrt{30}\right)^{2}.

$$\left(\frac{1}{10}\right)^{2}\left(\sqrt{30}\right)^{2}$$

Calculate \frac{1}{10} to the power of 2 and get \frac{1}{100}.

$$\frac{1}{100}\left(\sqrt{30}\right)^{2}$$

The square of \sqrt{30} is 30.

$$\frac{1}{100}\times 30$$

Multiply \frac{1}{100} and 30 to get \frac{3}{10}.

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

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$