Solve sqrt{(1/3+1/4):(2-2/7)}+sqrt{9/144}=

$$\sqrt { ( \frac { 1 } { 3 } + \frac { 1 } { 4 } ) : ( 2 - \frac { 2 } { 7 } ) } + \sqrt { \frac { 9 } { 144 } } =$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\sqrt{\frac{\frac{4}{12}+\frac{3}{12}}{2-\frac{2}{7}}}+\sqrt{\frac{9}{144}}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{4+3}{12}}{2-\frac{2}{7}}}+\sqrt{\frac{9}{144}}$$

Add 4 and 3 to get 7.

$$\sqrt{\frac{\frac{7}{12}}{2-\frac{2}{7}}}+\sqrt{\frac{9}{144}}$$

Convert 2 to fraction \frac{14}{7}.

$$\sqrt{\frac{\frac{7}{12}}{\frac{14}{7}-\frac{2}{7}}}+\sqrt{\frac{9}{144}}$$

Since \frac{14}{7} and \frac{2}{7} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{7}{12}}{\frac{14-2}{7}}}+\sqrt{\frac{9}{144}}$$

Subtract 2 from 14 to get 12.

$$\sqrt{\frac{\frac{7}{12}}{\frac{12}{7}}}+\sqrt{\frac{9}{144}}$$

Divide \frac{7}{12} by \frac{12}{7} by multiplying \frac{7}{12} by the reciprocal of \frac{12}{7}.

$$\sqrt{\frac{7}{12}\times \frac{7}{12}}+\sqrt{\frac{9}{144}}$$

Multiply \frac{7}{12} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{7\times 7}{12\times 12}}+\sqrt{\frac{9}{144}}$$

Do the multiplications in the fraction \frac{7\times 7}{12\times 12}.

$$\sqrt{\frac{49}{144}}+\sqrt{\frac{9}{144}}$$

Rewrite the square root of the division \frac{49}{144} as the division of square roots \frac{\sqrt{49}}{\sqrt{144}}. Take the square root of both numerator and denominator.

$$\frac{7}{12}+\sqrt{\frac{9}{144}}$$

Reduce the fraction \frac{9}{144} to lowest terms by extracting and canceling out 9.

$$\frac{7}{12}+\sqrt{\frac{1}{16}}$$

Rewrite the square root of the division \frac{1}{16} as the division of square roots \frac{\sqrt{1}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{7}{12}+\frac{1}{4}$$

Least common multiple of 12 and 4 is 12. Convert \frac{7}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{7}{12}+\frac{3}{12}$$

Since \frac{7}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{7+3}{12}$$

Add 7 and 3 to get 10.

$$\frac{10}{12}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$