Solve sqrt{49/64}+3,2-4/5+9,8+72/3

$$\sqrt { \frac { 49 } { 64 } } + 3,2 - \frac { 4 } { 5 } + 9,8 + \frac { 72 } { 3 }$$

Evaluate

$$37,075$$

Solution Steps

Rewrite the square root of the division \frac{49}{64} as the division of square roots \frac{\sqrt{49}}{\sqrt{64}}. Take the square root of both numerator and denominator.

$$\frac{7}{8}+3,2-\frac{4}{5}+9,8+\frac{72}{3}$$

Convert decimal number 3,2 to fraction \frac{32}{10}. Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{7}{8}+\frac{16}{5}-\frac{4}{5}+9,8+\frac{72}{3}$$

Least common multiple of 8 and 5 is 40. Convert \frac{7}{8} and \frac{16}{5} to fractions with denominator 40.

$$\frac{35}{40}+\frac{128}{40}-\frac{4}{5}+9,8+\frac{72}{3}$$

Since \frac{35}{40} and \frac{128}{40} have the same denominator, add them by adding their numerators.

$$\frac{35+128}{40}-\frac{4}{5}+9,8+\frac{72}{3}$$

Add 35 and 128 to get 163.

$$\frac{163}{40}-\frac{4}{5}+9,8+\frac{72}{3}$$

Least common multiple of 40 and 5 is 40. Convert \frac{163}{40} and \frac{4}{5} to fractions with denominator 40.

$$\frac{163}{40}-\frac{32}{40}+9,8+\frac{72}{3}$$

Since \frac{163}{40} and \frac{32}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{163-32}{40}+9,8+\frac{72}{3}$$

Subtract 32 from 163 to get 131.

$$\frac{131}{40}+9,8+\frac{72}{3}$$

Convert decimal number 9,8 to fraction \frac{98}{10}. Reduce the fraction \frac{98}{10} to lowest terms by extracting and canceling out 2.

$$\frac{131}{40}+\frac{49}{5}+\frac{72}{3}$$

Least common multiple of 40 and 5 is 40. Convert \frac{131}{40} and \frac{49}{5} to fractions with denominator 40.

$$\frac{131}{40}+\frac{392}{40}+\frac{72}{3}$$

Since \frac{131}{40} and \frac{392}{40} have the same denominator, add them by adding their numerators.

$$\frac{131+392}{40}+\frac{72}{3}$$

Add 131 and 392 to get 523.

$$\frac{523}{40}+\frac{72}{3}$$

Divide 72 by 3 to get 24.

$$\frac{523}{40}+24$$

Convert 24 to fraction \frac{960}{40}.

$$\frac{523}{40}+\frac{960}{40}$$

Since \frac{523}{40} and \frac{960}{40} have the same denominator, add them by adding their numerators.

$$\frac{523+960}{40}$$

Add 523 and 960 to get 1483.

$$\frac{1483}{40}$$

Factor

$$\frac{1483}{5 \cdot 2 ^ {3}} = 37\frac{3}{40} = 37.075$$