Solve sqrt{(2/12+3/15)}

$$\sqrt { ( \frac { 2 } { 12 } + \frac { 3 } { 15 } ) }$$

Evaluate

$$\frac{\sqrt{330}}{30}\approx 0.605530071$$

Solution Steps

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1}{6}+\frac{3}{15}}$$

Reduce the fraction \frac{3}{15} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{1}{6}+\frac{1}{5}}$$

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{1}{5} to fractions with denominator 30.

$$\sqrt{\frac{5}{30}+\frac{6}{30}}$$

Since \frac{5}{30} and \frac{6}{30} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{5+6}{30}}$$

Add 5 and 6 to get 11.

$$\sqrt{\frac{11}{30}}$$

Rewrite the square root of the division \sqrt{\frac{11}{30}} as the division of square roots \frac{\sqrt{11}}{\sqrt{30}}.

$$\frac{\sqrt{11}}{\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{\sqrt{11}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{\sqrt{11}\sqrt{30}}{30}$$

To multiply \sqrt{11} and \sqrt{30}, multiply the numbers under the square root.

$$\frac{\sqrt{330}}{30}$$