Solve sqrt{(2/5+3/10+2/15)*(7+7/2)}

$$\sqrt { ( \frac { 2 } { 5 } + \frac { 3 } { 10 } + \frac { 2 } { 15 } ) \cdot ( 7 + \frac { 7 } { 2 } ) }$$

Evaluate

$$\frac{\sqrt{35}}{2}\approx 2.958039892$$

Solution Steps

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{3}{10} to fractions with denominator 10.

$$\sqrt{\left(\frac{4}{10}+\frac{3}{10}+\frac{2}{15}\right)\left(7+\frac{7}{2}\right)}$$

Since \frac{4}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\sqrt{\left(\frac{4+3}{10}+\frac{2}{15}\right)\left(7+\frac{7}{2}\right)}$$

Add 4 and 3 to get 7.

$$\sqrt{\left(\frac{7}{10}+\frac{2}{15}\right)\left(7+\frac{7}{2}\right)}$$

Least common multiple of 10 and 15 is 30. Convert \frac{7}{10} and \frac{2}{15} to fractions with denominator 30.

$$\sqrt{\left(\frac{21}{30}+\frac{4}{30}\right)\left(7+\frac{7}{2}\right)}$$

Since \frac{21}{30} and \frac{4}{30} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{21+4}{30}\left(7+\frac{7}{2}\right)}$$

Add 21 and 4 to get 25.

$$\sqrt{\frac{25}{30}\left(7+\frac{7}{2}\right)}$$

Reduce the fraction \frac{25}{30} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{5}{6}\left(7+\frac{7}{2}\right)}$$

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

$$\sqrt{\frac{5}{6}\left(\frac{14}{2}+\frac{7}{2}\right)}$$

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

$$\sqrt{\frac{5}{6}\times \frac{14+7}{2}}$$

Add 14 and 7 to get 21.

$$\sqrt{\frac{5}{6}\times \frac{21}{2}}$$

Multiply \frac{5}{6} times \frac{21}{2} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{5\times 21}{6\times 2}}$$

Do the multiplications in the fraction \frac{5\times 21}{6\times 2}.

$$\sqrt{\frac{105}{12}}$$

Reduce the fraction \frac{105}{12} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{35}{4}}$$

Rewrite the square root of the division \sqrt{\frac{35}{4}} as the division of square roots \frac{\sqrt{35}}{\sqrt{4}}.

$$\frac{\sqrt{35}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{35}}{2}$$