Solve sqrt{[(35/6+25/12-6)*(2-26/15)+8/9]:(frac{1}{4}+1+frac{1}{2}-frac{7}{5})}

$$\sqrt { [ ( \frac { 35 } { 6 } + \frac { 25 } { 12 } - 6 ) \times ( 2 - \frac { 26 } { 15 } ) + \frac { 8 } { 9 } ] : ( \frac { 1 } { 4 } + 1 + \frac { 1 } { 2 } - \frac { 7 } { 5 } ) }$$

Evaluate

$$2$$

Solution Steps

Least common multiple of 6 and 12 is 12. Convert \frac{35}{6} and \frac{25}{12} to fractions with denominator 12.

$$\sqrt{\frac{\left(\frac{70}{12}+\frac{25}{12}-6\right)\left(2-\frac{26}{15}\right)+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Since \frac{70}{12} and \frac{25}{12} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\left(\frac{70+25}{12}-6\right)\left(2-\frac{26}{15}\right)+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Add 70 and 25 to get 95.

$$\sqrt{\frac{\left(\frac{95}{12}-6\right)\left(2-\frac{26}{15}\right)+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Convert 6 to fraction \frac{72}{12}.

$$\sqrt{\frac{\left(\frac{95}{12}-\frac{72}{12}\right)\left(2-\frac{26}{15}\right)+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Since \frac{95}{12} and \frac{72}{12} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{95-72}{12}\left(2-\frac{26}{15}\right)+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Subtract 72 from 95 to get 23.

$$\sqrt{\frac{\frac{23}{12}\left(2-\frac{26}{15}\right)+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Convert 2 to fraction \frac{30}{15}.

$$\sqrt{\frac{\frac{23}{12}\left(\frac{30}{15}-\frac{26}{15}\right)+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Since \frac{30}{15} and \frac{26}{15} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{23}{12}\times \frac{30-26}{15}+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Subtract 26 from 30 to get 4.

$$\sqrt{\frac{\frac{23}{12}\times \frac{4}{15}+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Multiply \frac{23}{12} times \frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{\frac{23\times 4}{12\times 15}+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Do the multiplications in the fraction \frac{23\times 4}{12\times 15}.

$$\sqrt{\frac{\frac{92}{180}+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Reduce the fraction \frac{92}{180} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{\frac{23}{45}+\frac{8}{9}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Least common multiple of 45 and 9 is 45. Convert \frac{23}{45} and \frac{8}{9} to fractions with denominator 45.

$$\sqrt{\frac{\frac{23}{45}+\frac{40}{45}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Since \frac{23}{45} and \frac{40}{45} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{23+40}{45}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Add 23 and 40 to get 63.

$$\sqrt{\frac{\frac{63}{45}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Reduce the fraction \frac{63}{45} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{\frac{7}{5}}{\frac{1}{4}+1+\frac{1}{2}-\frac{7}{5}}}$$

Convert 1 to fraction \frac{4}{4}.

$$\sqrt{\frac{\frac{7}{5}}{\frac{1}{4}+\frac{4}{4}+\frac{1}{2}-\frac{7}{5}}}$$

Since \frac{1}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{7}{5}}{\frac{1+4}{4}+\frac{1}{2}-\frac{7}{5}}}$$

Add 1 and 4 to get 5.

$$\sqrt{\frac{\frac{7}{5}}{\frac{5}{4}+\frac{1}{2}-\frac{7}{5}}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{1}{2} to fractions with denominator 4.

$$\sqrt{\frac{\frac{7}{5}}{\frac{5}{4}+\frac{2}{4}-\frac{7}{5}}}$$

Since \frac{5}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{7}{5}}{\frac{5+2}{4}-\frac{7}{5}}}$$

Add 5 and 2 to get 7.

$$\sqrt{\frac{\frac{7}{5}}{\frac{7}{4}-\frac{7}{5}}}$$

Least common multiple of 4 and 5 is 20. Convert \frac{7}{4} and \frac{7}{5} to fractions with denominator 20.

$$\sqrt{\frac{\frac{7}{5}}{\frac{35}{20}-\frac{28}{20}}}$$

Since \frac{35}{20} and \frac{28}{20} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{7}{5}}{\frac{35-28}{20}}}$$

Subtract 28 from 35 to get 7.

$$\sqrt{\frac{\frac{7}{5}}{\frac{7}{20}}}$$

Divide \frac{7}{5} by \frac{7}{20} by multiplying \frac{7}{5} by the reciprocal of \frac{7}{20}.

$$\sqrt{\frac{7}{5}\times \frac{20}{7}}$$

Multiply \frac{7}{5} times \frac{20}{7} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{7\times 20}{5\times 7}}$$

Cancel out 7 in both numerator and denominator.

$$\sqrt{\frac{20}{5}}$$

Divide 20 by 5 to get 4.

$$\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$2$$

Factor

$$2$$