Solve sqrt{[(2/9-1/3*2/3)*2/5+(frac{10}{18}-frac{1}{4}*frac{10}{9})*frac{9}{20}*frac{24}{3}]*[(frac{2}{5}+frac{3}{10})*frac{10}{7}]}

$$\sqrt { [ ( \frac { 2 } { 9 } - \frac { 1 } { 3 } \times \frac { 2 } { 3 } ) \times \frac { 2 } { 5 } + ( \frac { 10 } { 18 } - \frac { 1 } { 4 } \times \frac { 10 } { 9 } ) \times \frac { 9 } { 20 } \times \frac { 24 } { 3 } ] \times [ ( \frac { 2 } { 5 } + \frac { 3 } { 10 } ) \times \frac { 10 } { 7 } ] }$$

Evaluate

$$1$$

Solution Steps

Multiply \frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\left(\left(\frac{2}{9}-\frac{1\times 2}{3\times 3}\right)\times \frac{2}{5}+\left(\frac{10}{18}-\frac{1}{4}\times \frac{10}{9}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 3}.

$$\sqrt{\left(\left(\frac{2}{9}-\frac{2}{9}\right)\times \frac{2}{5}+\left(\frac{10}{18}-\frac{1}{4}\times \frac{10}{9}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Subtract \frac{2}{9} from \frac{2}{9} to get 0.

$$\sqrt{\left(0\times \frac{2}{5}+\left(\frac{10}{18}-\frac{1}{4}\times \frac{10}{9}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Multiply 0 and \frac{2}{5} to get 0.

$$\sqrt{\left(0+\left(\frac{10}{18}-\frac{1}{4}\times \frac{10}{9}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Reduce the fraction \frac{10}{18} to lowest terms by extracting and canceling out 2.

$$\sqrt{\left(0+\left(\frac{5}{9}-\frac{1}{4}\times \frac{10}{9}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Multiply \frac{1}{4} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\left(0+\left(\frac{5}{9}-\frac{1\times 10}{4\times 9}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Do the multiplications in the fraction \frac{1\times 10}{4\times 9}.

$$\sqrt{\left(0+\left(\frac{5}{9}-\frac{10}{36}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Reduce the fraction \frac{10}{36} to lowest terms by extracting and canceling out 2.

$$\sqrt{\left(0+\left(\frac{5}{9}-\frac{5}{18}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Least common multiple of 9 and 18 is 18. Convert \frac{5}{9} and \frac{5}{18} to fractions with denominator 18.

$$\sqrt{\left(0+\left(\frac{10}{18}-\frac{5}{18}\right)\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Since \frac{10}{18} and \frac{5}{18} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\left(0+\frac{10-5}{18}\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Subtract 5 from 10 to get 5.

$$\sqrt{\left(0+\frac{5}{18}\times \frac{9}{20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Multiply \frac{5}{18} times \frac{9}{20} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\left(0+\frac{5\times 9}{18\times 20}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Do the multiplications in the fraction \frac{5\times 9}{18\times 20}.

$$\sqrt{\left(0+\frac{45}{360}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Reduce the fraction \frac{45}{360} to lowest terms by extracting and canceling out 45.

$$\sqrt{\left(0+\frac{1}{8}\times \frac{24}{3}\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Divide 24 by 3 to get 8.

$$\sqrt{\left(0+\frac{1}{8}\times 8\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Cancel out 8 and 8.

$$\sqrt{\left(0+1\right)\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

Add 0 and 1 to get 1.

$$\sqrt{1\left(\frac{2}{5}+\frac{3}{10}\right)\times \frac{10}{7}}$$

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

$$\sqrt{1\left(\frac{4}{10}+\frac{3}{10}\right)\times \frac{10}{7}}$$

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

$$\sqrt{1\times \frac{4+3}{10}\times \frac{10}{7}}$$

Add 4 and 3 to get 7.

$$\sqrt{1\times \frac{7}{10}\times \frac{10}{7}}$$

Multiply 1 and \frac{7}{10} to get \frac{7}{10}.

$$\sqrt{\frac{7}{10}\times \frac{10}{7}}$$

Cancel out \frac{7}{10} and its reciprocal \frac{10}{7}.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$