Solve sqrt{5/3}+sqrt{5/6}

$$\sqrt{ \frac{ 5 }{ 3 } } + \sqrt{ \frac{ 5 }{ 6 } }$$

Evaluate

$$\frac{\sqrt{30}+2\sqrt{15}}{6}\approx 2.203865378$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

$$\frac{\sqrt{5}}{\sqrt{3}}+\sqrt{\frac{5}{6}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{\frac{5}{6}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{5}\sqrt{3}}{3}+\sqrt{\frac{5}{6}}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{3}+\sqrt{\frac{5}{6}}$$

Rewrite the square root of the division \sqrt{\frac{5}{6}} as the division of square roots \frac{\sqrt{5}}{\sqrt{6}}.

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{5}}{\sqrt{6}}$$

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

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{5}\sqrt{6}}{6}$$

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

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{30}}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 6 is 6. Multiply \frac{\sqrt{15}}{3} times \frac{2}{2}.

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

Since \frac{2\sqrt{15}}{6} and \frac{\sqrt{30}}{6} have the same denominator, add them by adding their numerators.

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