Solve 8sqrt{0,49}-3/7*sqrt{54/9}-9/64*sqrt{7744/9801}

$$8 \sqrt { 0,49 } - \frac { 3 } { 7 } \cdot \sqrt { 5 \frac { 4 } { 9 } } - \frac { 9 } { 64 } \cdot \sqrt { \frac { 7744 } { 9801 } }$$

Evaluate

$$4,475$$

Solution Steps

Calculate the square root of 0,49 and get 0,7.

$$8\times 0,7-\frac{3}{7}\sqrt{\frac{5\times 9+4}{9}}-\frac{9}{64}\sqrt{\frac{7744}{9801}}$$

Multiply 8 and 0,7 to get 5,6.

$$5,6-\frac{3}{7}\sqrt{\frac{5\times 9+4}{9}}-\frac{9}{64}\sqrt{\frac{7744}{9801}}$$

Multiply 5 and 9 to get 45.

$$5,6-\frac{3}{7}\sqrt{\frac{45+4}{9}}-\frac{9}{64}\sqrt{\frac{7744}{9801}}$$

Add 45 and 4 to get 49.

$$5,6-\frac{3}{7}\sqrt{\frac{49}{9}}-\frac{9}{64}\sqrt{\frac{7744}{9801}}$$

Rewrite the square root of the division \frac{49}{9} as the division of square roots \frac{\sqrt{49}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$5,6-\frac{3}{7}\times \frac{7}{3}-\frac{9}{64}\sqrt{\frac{7744}{9801}}$$

Cancel out \frac{3}{7} and its reciprocal \frac{7}{3}.

$$5,6-1-\frac{9}{64}\sqrt{\frac{7744}{9801}}$$

Subtract 1 from 5,6 to get 4,6.

$$4,6-\frac{9}{64}\sqrt{\frac{7744}{9801}}$$

Reduce the fraction \frac{7744}{9801} to lowest terms by extracting and canceling out 121.

$$4,6-\frac{9}{64}\sqrt{\frac{64}{81}}$$

Rewrite the square root of the division \frac{64}{81} as the division of square roots \frac{\sqrt{64}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$4,6-\frac{9}{64}\times \frac{8}{9}$$

Multiply \frac{9}{64} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$4,6-\frac{9\times 8}{64\times 9}$$

Cancel out 9 in both numerator and denominator.

$$4,6-\frac{8}{64}$$

Reduce the fraction \frac{8}{64} to lowest terms by extracting and canceling out 8.

$$4,6-\frac{1}{8}$$

Convert decimal number 4,6 to fraction \frac{46}{10}. Reduce the fraction \frac{46}{10} to lowest terms by extracting and canceling out 2.

$$\frac{23}{5}-\frac{1}{8}$$

Least common multiple of 5 and 8 is 40. Convert \frac{23}{5} and \frac{1}{8} to fractions with denominator 40.

$$\frac{184}{40}-\frac{5}{40}$$

Since \frac{184}{40} and \frac{5}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{184-5}{40}$$

Subtract 5 from 184 to get 179.

$$\frac{179}{40}$$

Factor

$$\frac{179}{5 \cdot 2 ^ {3}} = 4\frac{19}{40} = 4.475$$