Solve sqrt{4/3+1/9-1/12}

$$\sqrt { \frac { 4 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 12 } }$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{1}{9} to fractions with denominator 9.

$$\sqrt{\frac{12}{9}+\frac{1}{9}-\frac{1}{12}}$$

Since \frac{12}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{12+1}{9}-\frac{1}{12}}$$

Add 12 and 1 to get 13.

$$\sqrt{\frac{13}{9}-\frac{1}{12}}$$

Least common multiple of 9 and 12 is 36. Convert \frac{13}{9} and \frac{1}{12} to fractions with denominator 36.

$$\sqrt{\frac{52}{36}-\frac{3}{36}}$$

Since \frac{52}{36} and \frac{3}{36} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{52-3}{36}}$$

Subtract 3 from 52 to get 49.

$$\sqrt{\frac{49}{36}}$$

Rewrite the square root of the division \frac{49}{36} as the division of square roots \frac{\sqrt{49}}{\sqrt{36}}. Take the square root of both numerator and denominator.

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

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$