Solve sqrt{(7/8-1/12+2/6)-{9/8-[frac{45}{12}-(frac{15}{28}+frac{11}{4}-frac{2}{7})]}+[frac{4}{3}+(frac{15}{4}-frac{25}{12})-(12-frac{21}{2})]}=

$$\sqrt { ( \frac { 7 } { 8 } - \frac { 1 } { 12 } + \frac { 2 } { 6 } ) - \{ \frac { 9 } { 8 } - [ \frac { 45 } { 12 } - ( \frac { 15 } { 28 } + \frac { 11 } { 4 } - \frac { 2 } { 7 } ) ] \} + [ \frac { 4 } { 3 } + ( \frac { 15 } { 4 } - \frac { 25 } { 12 } ) - ( 12 - \frac { 21 } { 2 } ) ] } =$$

Evaluate

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

Solution Steps

Least common multiple of 8 and 12 is 24. Convert \frac{7}{8} and \frac{1}{12} to fractions with denominator 24.

$$\sqrt{\frac{21}{24}-\frac{2}{24}+\frac{2}{6}-\left(\frac{9}{8}-\left(\frac{45}{12}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{21}{24} and \frac{2}{24} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{21-2}{24}+\frac{2}{6}-\left(\frac{9}{8}-\left(\frac{45}{12}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Subtract 2 from 21 to get 19.

$$\sqrt{\frac{19}{24}+\frac{2}{6}-\left(\frac{9}{8}-\left(\frac{45}{12}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

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

$$\sqrt{\frac{19}{24}+\frac{1}{3}-\left(\frac{9}{8}-\left(\frac{45}{12}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Least common multiple of 24 and 3 is 24. Convert \frac{19}{24} and \frac{1}{3} to fractions with denominator 24.

$$\sqrt{\frac{19}{24}+\frac{8}{24}-\left(\frac{9}{8}-\left(\frac{45}{12}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{19}{24} and \frac{8}{24} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{19+8}{24}-\left(\frac{9}{8}-\left(\frac{45}{12}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Add 19 and 8 to get 27.

$$\sqrt{\frac{27}{24}-\left(\frac{9}{8}-\left(\frac{45}{12}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Reduce the fraction \frac{27}{24} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{45}{12}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Reduce the fraction \frac{45}{12} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-\left(\frac{15}{28}+\frac{11}{4}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Least common multiple of 28 and 4 is 28. Convert \frac{15}{28} and \frac{11}{4} to fractions with denominator 28.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-\left(\frac{15}{28}+\frac{77}{28}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{15}{28} and \frac{77}{28} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-\left(\frac{15+77}{28}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Add 15 and 77 to get 92.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-\left(\frac{92}{28}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Reduce the fraction \frac{92}{28} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-\left(\frac{23}{7}-\frac{2}{7}\right)\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{23}{7} and \frac{2}{7} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-\frac{23-2}{7}\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Subtract 2 from 23 to get 21.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-\frac{21}{7}\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Divide 21 by 7 to get 3.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-3\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Convert 3 to fraction \frac{12}{4}.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\left(\frac{15}{4}-\frac{12}{4}\right)\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{15}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\frac{15-12}{4}\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Subtract 12 from 15 to get 3.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\frac{3}{4}\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Least common multiple of 8 and 4 is 8. Convert \frac{9}{8} and \frac{3}{4} to fractions with denominator 8.

$$\sqrt{\frac{9}{8}-\left(\frac{9}{8}-\frac{6}{8}\right)+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{9}{8} and \frac{6}{8} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{9}{8}-\frac{9-6}{8}+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Subtract 6 from 9 to get 3.

$$\sqrt{\frac{9}{8}-\frac{3}{8}+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{9}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{9-3}{8}+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Subtract 3 from 9 to get 6.

$$\sqrt{\frac{6}{8}+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{3}{4}+\frac{4}{3}+\frac{15}{4}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Least common multiple of 3 and 4 is 12. Convert \frac{4}{3} and \frac{15}{4} to fractions with denominator 12.

$$\sqrt{\frac{3}{4}+\frac{16}{12}+\frac{45}{12}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{16}{12} and \frac{45}{12} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{3}{4}+\frac{16+45}{12}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Add 16 and 45 to get 61.

$$\sqrt{\frac{3}{4}+\frac{61}{12}-\frac{25}{12}-\left(12-\frac{21}{2}\right)}$$

Since \frac{61}{12} and \frac{25}{12} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{3}{4}+\frac{61-25}{12}-\left(12-\frac{21}{2}\right)}$$

Subtract 25 from 61 to get 36.

$$\sqrt{\frac{3}{4}+\frac{36}{12}-\left(12-\frac{21}{2}\right)}$$

Divide 36 by 12 to get 3.

$$\sqrt{\frac{3}{4}+3-\left(12-\frac{21}{2}\right)}$$

Convert 12 to fraction \frac{24}{2}.

$$\sqrt{\frac{3}{4}+3-\left(\frac{24}{2}-\frac{21}{2}\right)}$$

Since \frac{24}{2} and \frac{21}{2} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{3}{4}+3-\frac{24-21}{2}}$$

Subtract 21 from 24 to get 3.

$$\sqrt{\frac{3}{4}+3-\frac{3}{2}}$$

Convert 3 to fraction \frac{6}{2}.

$$\sqrt{\frac{3}{4}+\frac{6}{2}-\frac{3}{2}}$$

Since \frac{6}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{3}{4}+\frac{6-3}{2}}$$

Subtract 3 from 6 to get 3.

$$\sqrt{\frac{3}{4}+\frac{3}{2}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{3}{2} to fractions with denominator 4.

$$\sqrt{\frac{3}{4}+\frac{6}{4}}$$

Since \frac{3}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{3+6}{4}}$$

Add 3 and 6 to get 9.

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

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

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