Solve sqrt{(1/2-9/26)*[5/13-1/2:(frac{5}{3}+frac{1}{2})]}=

$$\sqrt { ( \frac { 1 } { 2 } - \frac { 9 } { 26 } ) \cdot [ \frac { 5 } { 13 } - \frac { 1 } { 2 } : ( \frac { 5 } { 3 } + \frac { 1 } { 2 } ) ] } =$$

Evaluate

$$\frac{2}{13}\approx 0.153846154$$

Solution Steps

Least common multiple of 2 and 26 is 26. Convert \frac{1}{2} and \frac{9}{26} to fractions with denominator 26.

$$\sqrt{\left(\frac{13}{26}-\frac{9}{26}\right)\left(\frac{5}{13}-\frac{\frac{1}{2}}{\frac{5}{3}+\frac{1}{2}}\right)}$$

Since \frac{13}{26} and \frac{9}{26} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{13-9}{26}\left(\frac{5}{13}-\frac{\frac{1}{2}}{\frac{5}{3}+\frac{1}{2}}\right)}$$

Subtract 9 from 13 to get 4.

$$\sqrt{\frac{4}{26}\left(\frac{5}{13}-\frac{\frac{1}{2}}{\frac{5}{3}+\frac{1}{2}}\right)}$$

Reduce the fraction \frac{4}{26} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{2}{13}\left(\frac{5}{13}-\frac{\frac{1}{2}}{\frac{5}{3}+\frac{1}{2}}\right)}$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{1}{2} to fractions with denominator 6.

$$\sqrt{\frac{2}{13}\left(\frac{5}{13}-\frac{\frac{1}{2}}{\frac{10}{6}+\frac{3}{6}}\right)}$$

Since \frac{10}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{2}{13}\left(\frac{5}{13}-\frac{\frac{1}{2}}{\frac{10+3}{6}}\right)}$$

Add 10 and 3 to get 13.

$$\sqrt{\frac{2}{13}\left(\frac{5}{13}-\frac{\frac{1}{2}}{\frac{13}{6}}\right)}$$

Divide \frac{1}{2} by \frac{13}{6} by multiplying \frac{1}{2} by the reciprocal of \frac{13}{6}.

$$\sqrt{\frac{2}{13}\left(\frac{5}{13}-\frac{1}{2}\times \frac{6}{13}\right)}$$

Multiply \frac{1}{2} times \frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{2}{13}\left(\frac{5}{13}-\frac{1\times 6}{2\times 13}\right)}$$

Do the multiplications in the fraction \frac{1\times 6}{2\times 13}.

$$\sqrt{\frac{2}{13}\left(\frac{5}{13}-\frac{6}{26}\right)}$$

Reduce the fraction \frac{6}{26} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{2}{13}\left(\frac{5}{13}-\frac{3}{13}\right)}$$

Since \frac{5}{13} and \frac{3}{13} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{2}{13}\times \frac{5-3}{13}}$$

Subtract 3 from 5 to get 2.

$$\sqrt{\frac{2}{13}\times \frac{2}{13}}$$

Multiply \frac{2}{13} times \frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{2\times 2}{13\times 13}}$$

Do the multiplications in the fraction \frac{2\times 2}{13\times 13}.

$$\sqrt{\frac{4}{169}}$$

Rewrite the square root of the division \frac{4}{169} as the division of square roots \frac{\sqrt{4}}{\sqrt{169}}. Take the square root of both numerator and denominator.

$$\frac{2}{13}$$

Factor

$$\frac{2}{13} = 0.15384615384615385$$