Solve sqrt{79/36+7/18-5/6*2/5}

$$\sqrt { \frac { 79 } { 36 } + \frac { 7 } { 18 } - \frac { 5 } { 6 } \cdot \frac { 2 } { 5 } }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Least common multiple of 36 and 18 is 36. Convert \frac{79}{36} and \frac{7}{18} to fractions with denominator 36.

$$\sqrt{\frac{79}{36}+\frac{14}{36}-\frac{5}{6}\times \frac{2}{5}}$$

Since \frac{79}{36} and \frac{14}{36} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{79+14}{36}-\frac{5}{6}\times \frac{2}{5}}$$

Add 79 and 14 to get 93.

$$\sqrt{\frac{93}{36}-\frac{5}{6}\times \frac{2}{5}}$$

Reduce the fraction \frac{93}{36} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{31}{12}-\frac{5}{6}\times \frac{2}{5}}$$

Multiply \frac{5}{6} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{31}{12}-\frac{5\times 2}{6\times 5}}$$

Cancel out 5 in both numerator and denominator.

$$\sqrt{\frac{31}{12}-\frac{2}{6}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{31}{12}-\frac{1}{3}}$$

Least common multiple of 12 and 3 is 12. Convert \frac{31}{12} and \frac{1}{3} to fractions with denominator 12.

$$\sqrt{\frac{31}{12}-\frac{4}{12}}$$

Since \frac{31}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{31-4}{12}}$$

Subtract 4 from 31 to get 27.

$$\sqrt{\frac{27}{12}}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{9}{4}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$