Solve sqrt{1/3+2/5}

$$\sqrt { \frac { 1 } { 3 } + \frac { 2 } { 5 } }$$

Evaluate

$$\frac{\sqrt{165}}{15}\approx 0.856348839$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

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

Since \frac{5}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

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

Add 5 and 6 to get 11.

$$\sqrt{\frac{11}{15}}$$

Rewrite the square root of the division \sqrt{\frac{11}{15}} as the division of square roots \frac{\sqrt{11}}{\sqrt{15}}.

$$\frac{\sqrt{11}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{11}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{11}\sqrt{15}}{15}$$

To multiply \sqrt{11} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{165}}{15}$$