Solve sqrt{4/3*[3/2:(1-1/8+3/4*frac{35}{18}-frac{1}{3})}]

$$\sqrt { \frac { 4 } { 3 } \times [ \frac { 3 } { 2 } : ( 1 - \frac { 1 } { 8 } + \frac { 3 } { 4 } \times \frac { 35 } { 18 } - \frac { 1 } { 3 } ) } ]$$

Evaluate

$$1$$

Solution Steps

Convert 1 to fraction \frac{8}{8}.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{8}{8}-\frac{1}{8}+\frac{3}{4}\times \frac{35}{18}-\frac{1}{3}}}$$

Since \frac{8}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{8-1}{8}+\frac{3}{4}\times \frac{35}{18}-\frac{1}{3}}}$$

Subtract 1 from 8 to get 7.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{7}{8}+\frac{3}{4}\times \frac{35}{18}-\frac{1}{3}}}$$

Multiply \frac{3}{4} times \frac{35}{18} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{7}{8}+\frac{3\times 35}{4\times 18}-\frac{1}{3}}}$$

Do the multiplications in the fraction \frac{3\times 35}{4\times 18}.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{7}{8}+\frac{105}{72}-\frac{1}{3}}}$$

Reduce the fraction \frac{105}{72} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{7}{8}+\frac{35}{24}-\frac{1}{3}}}$$

Least common multiple of 8 and 24 is 24. Convert \frac{7}{8} and \frac{35}{24} to fractions with denominator 24.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{21}{24}+\frac{35}{24}-\frac{1}{3}}}$$

Since \frac{21}{24} and \frac{35}{24} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{21+35}{24}-\frac{1}{3}}}$$

Add 21 and 35 to get 56.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{56}{24}-\frac{1}{3}}}$$

Reduce the fraction \frac{56}{24} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{7}{3}-\frac{1}{3}}}$$

Since \frac{7}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{7-1}{3}}}$$

Subtract 1 from 7 to get 6.

$$\sqrt{\frac{4}{3}\times \frac{\frac{3}{2}}{\frac{6}{3}}}$$

Divide 6 by 3 to get 2.

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

Express \frac{\frac{3}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

$$\sqrt{\frac{4}{3}\times \frac{3}{4}}$$

Cancel out \frac{4}{3} and its reciprocal \frac{3}{4}.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$