Solve sqrt{1/2+1/3}=

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

Evaluate

$$\frac{\sqrt{30}}{6}\approx 0.912870929$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\sqrt{\frac{3}{6}+\frac{2}{6}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{3+2}{6}}$$

Add 3 and 2 to get 5.

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

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

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

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

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

The square of \sqrt{6} is 6.

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

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

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