Solve =359*sqrt{1-4/5*{(3/5)^2*5/3+1/11*[(frac{1}{4}+frac{3}{2})-frac{3}{4}*(frac{1}{3}-frac{1}{5})]+frac{1}{2}}}

$$= 359 \cdot \sqrt { 1 - \frac { 4 } { 5 } \times \{ ( \frac { 3 } { 5 } ) ^ { 2 } \times \frac { 5 } { 3 } + \frac { 1 } { 11 } \times [ ( \frac { 1 } { 4 } + \frac { 3 } { 2 } ) - \frac { 3 } { 4 } \times ( \frac { 1 } { 3 } - \frac { 1 } { 5 } ) ] + \frac { 1 } { 2 } \} }$$

Evaluate

$$0$$

Solution Steps

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$359\sqrt{1-\frac{4}{5}\left(\frac{9}{25}\times \frac{5}{3}+\frac{1}{11}\left(\frac{1}{4}+\frac{3}{2}-\frac{3}{4}\left(\frac{1}{3}-\frac{1}{5}\right)\right)+\frac{1}{2}\right)}$$

Multiply \frac{9}{25} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$359\sqrt{1-\frac{4}{5}\left(\frac{9\times 5}{25\times 3}+\frac{1}{11}\left(\frac{1}{4}+\frac{3}{2}-\frac{3}{4}\left(\frac{1}{3}-\frac{1}{5}\right)\right)+\frac{1}{2}\right)}$$

Do the multiplications in the fraction \frac{9\times 5}{25\times 3}.

$$359\sqrt{1-\frac{4}{5}\left(\frac{45}{75}+\frac{1}{11}\left(\frac{1}{4}+\frac{3}{2}-\frac{3}{4}\left(\frac{1}{3}-\frac{1}{5}\right)\right)+\frac{1}{2}\right)}$$

Reduce the fraction \frac{45}{75} to lowest terms by extracting and canceling out 15.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{1}{4}+\frac{3}{2}-\frac{3}{4}\left(\frac{1}{3}-\frac{1}{5}\right)\right)+\frac{1}{2}\right)}$$

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{3}{2} to fractions with denominator 4.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{1}{4}+\frac{6}{4}-\frac{3}{4}\left(\frac{1}{3}-\frac{1}{5}\right)\right)+\frac{1}{2}\right)}$$

Since \frac{1}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{1+6}{4}-\frac{3}{4}\left(\frac{1}{3}-\frac{1}{5}\right)\right)+\frac{1}{2}\right)}$$

Add 1 and 6 to get 7.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{7}{4}-\frac{3}{4}\left(\frac{1}{3}-\frac{1}{5}\right)\right)+\frac{1}{2}\right)}$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{7}{4}-\frac{3}{4}\left(\frac{5}{15}-\frac{3}{15}\right)\right)+\frac{1}{2}\right)}$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{7}{4}-\frac{3}{4}\times \frac{5-3}{15}\right)+\frac{1}{2}\right)}$$

Subtract 3 from 5 to get 2.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{7}{4}-\frac{3}{4}\times \frac{2}{15}\right)+\frac{1}{2}\right)}$$

Multiply \frac{3}{4} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{7}{4}-\frac{3\times 2}{4\times 15}\right)+\frac{1}{2}\right)}$$

Do the multiplications in the fraction \frac{3\times 2}{4\times 15}.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{7}{4}-\frac{6}{60}\right)+\frac{1}{2}\right)}$$

Reduce the fraction \frac{6}{60} to lowest terms by extracting and canceling out 6.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{7}{4}-\frac{1}{10}\right)+\frac{1}{2}\right)}$$

Least common multiple of 4 and 10 is 20. Convert \frac{7}{4} and \frac{1}{10} to fractions with denominator 20.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\left(\frac{35}{20}-\frac{2}{20}\right)+\frac{1}{2}\right)}$$

Since \frac{35}{20} and \frac{2}{20} have the same denominator, subtract them by subtracting their numerators.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\times \frac{35-2}{20}+\frac{1}{2}\right)}$$

Subtract 2 from 35 to get 33.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1}{11}\times \frac{33}{20}+\frac{1}{2}\right)}$$

Multiply \frac{1}{11} times \frac{33}{20} by multiplying numerator times numerator and denominator times denominator.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{1\times 33}{11\times 20}+\frac{1}{2}\right)}$$

Do the multiplications in the fraction \frac{1\times 33}{11\times 20}.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{33}{220}+\frac{1}{2}\right)}$$

Reduce the fraction \frac{33}{220} to lowest terms by extracting and canceling out 11.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{5}+\frac{3}{20}+\frac{1}{2}\right)}$$

Least common multiple of 5 and 20 is 20. Convert \frac{3}{5} and \frac{3}{20} to fractions with denominator 20.

$$359\sqrt{1-\frac{4}{5}\left(\frac{12}{20}+\frac{3}{20}+\frac{1}{2}\right)}$$

Since \frac{12}{20} and \frac{3}{20} have the same denominator, add them by adding their numerators.

$$359\sqrt{1-\frac{4}{5}\left(\frac{12+3}{20}+\frac{1}{2}\right)}$$

Add 12 and 3 to get 15.

$$359\sqrt{1-\frac{4}{5}\left(\frac{15}{20}+\frac{1}{2}\right)}$$

Reduce the fraction \frac{15}{20} to lowest terms by extracting and canceling out 5.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{4}+\frac{1}{2}\right)}$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$359\sqrt{1-\frac{4}{5}\left(\frac{3}{4}+\frac{2}{4}\right)}$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$359\sqrt{1-\frac{4}{5}\times \frac{3+2}{4}}$$

Add 3 and 2 to get 5.

$$359\sqrt{1-\frac{4}{5}\times \frac{5}{4}}$$

Cancel out \frac{4}{5} and its reciprocal \frac{5}{4}.

$$359\sqrt{1-1}$$

Subtract 1 from 1 to get 0.

$$359\sqrt{0}$$

Calculate the square root of 0 and get 0.

$$359\times 0$$

Multiply 359 and 0 to get 0.

$$0$$

Factor

$$0$$