Solve sqrt{2/3+1/2}

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

Evaluate

$$\frac{\sqrt{42}}{6}\approx 1.08012345$$

Solution Steps

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

$$\sqrt{\frac{4}{6}+\frac{3}{6}}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{4+3}{6}}$$

Add 4 and 3 to get 7.

$$\sqrt{\frac{7}{6}}$$

Rewrite the square root of the division \sqrt{\frac{7}{6}} as the division of square roots \frac{\sqrt{7}}{\sqrt{6}}.

$$\frac{\sqrt{7}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{7}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{7}\sqrt{6}}{6}$$

To multiply \sqrt{7} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{42}}{6}$$