Solve sqrt{118/27+19/2}

$$\sqrt { 1 \frac { 18 } { 27 } + \frac { 19 } { 2 } }$$

Evaluate

$$\frac{\sqrt{402}}{6}\approx 3.341656276$$

Solution Steps

Multiply 1 and 27 to get 27.

$$\sqrt{\frac{27+18}{27}+\frac{19}{2}}$$

Add 27 and 18 to get 45.

$$\sqrt{\frac{45}{27}+\frac{19}{2}}$$

Reduce the fraction \frac{45}{27} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{5}{3}+\frac{19}{2}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{19}{2} to fractions with denominator 6.

$$\sqrt{\frac{10}{6}+\frac{57}{6}}$$

Since \frac{10}{6} and \frac{57}{6} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{10+57}{6}}$$

Add 10 and 57 to get 67.

$$\sqrt{\frac{67}{6}}$$

Rewrite the square root of the division \sqrt{\frac{67}{6}} as the division of square roots \frac{\sqrt{67}}{\sqrt{6}}.

$$\frac{\sqrt{67}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{67}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{67}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{67}\sqrt{6}}{6}$$

To multiply \sqrt{67} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{402}}{6}$$