Solve sqrt{3/2*(5/4-10/9)+1/16-(frac{1}{2}-frac{7}{18}):frac{16}{3}}=

$$\sqrt { \frac { 3 } { 2 } \cdot ( \frac { 5 } { 4 } - \frac { 10 } { 9 } ) + \frac { 1 } { 16 } - ( \frac { 1 } { 2 } - \frac { 7 } { 18 } ) : \frac { 16 } { 3 } } =$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Least common multiple of 4 and 9 is 36. Convert \frac{5}{4} and \frac{10}{9} to fractions with denominator 36.

$$\sqrt{\frac{3}{2}\left(\frac{45}{36}-\frac{40}{36}\right)+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Since \frac{45}{36} and \frac{40}{36} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{3}{2}\times \frac{45-40}{36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Subtract 40 from 45 to get 5.

$$\sqrt{\frac{3}{2}\times \frac{5}{36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Multiply \frac{3}{2} times \frac{5}{36} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{3\times 5}{2\times 36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Do the multiplications in the fraction \frac{3\times 5}{2\times 36}.

$$\sqrt{\frac{15}{72}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Reduce the fraction \frac{15}{72} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{5}{24}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Least common multiple of 24 and 16 is 48. Convert \frac{5}{24} and \frac{1}{16} to fractions with denominator 48.

$$\sqrt{\frac{10}{48}+\frac{3}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Since \frac{10}{48} and \frac{3}{48} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{10+3}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Add 10 and 3 to get 13.

$$\sqrt{\frac{13}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Least common multiple of 2 and 18 is 18. Convert \frac{1}{2} and \frac{7}{18} to fractions with denominator 18.

$$\sqrt{\frac{13}{48}-\frac{\frac{9}{18}-\frac{7}{18}}{\frac{16}{3}}}$$

Since \frac{9}{18} and \frac{7}{18} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{13}{48}-\frac{\frac{9-7}{18}}{\frac{16}{3}}}$$

Subtract 7 from 9 to get 2.

$$\sqrt{\frac{13}{48}-\frac{\frac{2}{18}}{\frac{16}{3}}}$$

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

$$\sqrt{\frac{13}{48}-\frac{\frac{1}{9}}{\frac{16}{3}}}$$

Divide \frac{1}{9} by \frac{16}{3} by multiplying \frac{1}{9} by the reciprocal of \frac{16}{3}.

$$\sqrt{\frac{13}{48}-\frac{1}{9}\times \frac{3}{16}}$$

Multiply \frac{1}{9} times \frac{3}{16} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{13}{48}-\frac{1\times 3}{9\times 16}}$$

Do the multiplications in the fraction \frac{1\times 3}{9\times 16}.

$$\sqrt{\frac{13}{48}-\frac{3}{144}}$$

Reduce the fraction \frac{3}{144} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{13}{48}-\frac{1}{48}}$$

Since \frac{13}{48} and \frac{1}{48} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{13-1}{48}}$$

Subtract 1 from 13 to get 12.

$$\sqrt{\frac{12}{48}}$$

Reduce the fraction \frac{12}{48} to lowest terms by extracting and canceling out 12.

$$\sqrt{\frac{1}{4}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$