Solve sqrt{(3/4-1/6):(1-5/12)}

$$\sqrt { ( \frac { 3 } { 4 } - \frac { 1 } { 6 } ) : ( 1 - \frac { 5 } { 12 } ) }$$

Evaluate

$$1$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\sqrt{\frac{\frac{9}{12}-\frac{2}{12}}{1-\frac{5}{12}}}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{9-2}{12}}{1-\frac{5}{12}}}$$

Subtract 2 from 9 to get 7.

$$\sqrt{\frac{\frac{7}{12}}{1-\frac{5}{12}}}$$

Convert 1 to fraction \frac{12}{12}.

$$\sqrt{\frac{\frac{7}{12}}{\frac{12}{12}-\frac{5}{12}}}$$

Since \frac{12}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{7}{12}}{\frac{12-5}{12}}}$$

Subtract 5 from 12 to get 7.

$$\sqrt{\frac{\frac{7}{12}}{\frac{7}{12}}}$$

Divide \frac{7}{12} by \frac{7}{12} to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$