Solve 2*2*3.14*3.14*100left(1.004+0.2285/2right)/20.44^2

$$\frac{ 2 \cdot 2 \cdot 3.14 \cdot 3.14 \cdot 100 \left( 1.004+ \frac{ 0.2285 }{ 2 } \right) }{ { 20.44 }^{ 2 } }$$

Evaluate

$$\frac{15750711}{1492120}\approx 10.555927807$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4\times 3.14\times 3.14\times 100\left(1.004+\frac{0.2285}{2}\right)}{20.44^{2}}$$

Multiply 4 and 3.14 to get 12.56.

$$\frac{12.56\times 3.14\times 100\left(1.004+\frac{0.2285}{2}\right)}{20.44^{2}}$$

Multiply 12.56 and 3.14 to get 39.4384.

$$\frac{39.4384\times 100\left(1.004+\frac{0.2285}{2}\right)}{20.44^{2}}$$

Multiply 39.4384 and 100 to get 3943.84.

$$\frac{3943.84\left(1.004+\frac{0.2285}{2}\right)}{20.44^{2}}$$

Expand \frac{0.2285}{2} by multiplying both numerator and the denominator by 10000.

$$\frac{3943.84\left(1.004+\frac{2285}{20000}\right)}{20.44^{2}}$$

Reduce the fraction \frac{2285}{20000} to lowest terms by extracting and canceling out 5.

$$\frac{3943.84\left(1.004+\frac{457}{4000}\right)}{20.44^{2}}$$

Convert decimal number 1.004 to fraction \frac{1004}{1000}. Reduce the fraction \frac{1004}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{3943.84\left(\frac{251}{250}+\frac{457}{4000}\right)}{20.44^{2}}$$

Least common multiple of 250 and 4000 is 4000. Convert \frac{251}{250} and \frac{457}{4000} to fractions with denominator 4000.

$$\frac{3943.84\left(\frac{4016}{4000}+\frac{457}{4000}\right)}{20.44^{2}}$$

Since \frac{4016}{4000} and \frac{457}{4000} have the same denominator, add them by adding their numerators.

$$\frac{3943.84\times \frac{4016+457}{4000}}{20.44^{2}}$$

Add 4016 and 457 to get 4473.

$$\frac{3943.84\times \frac{4473}{4000}}{20.44^{2}}$$

Convert decimal number 3943.84 to fraction \frac{394384}{100}. Reduce the fraction \frac{394384}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{98596}{25}\times \frac{4473}{4000}}{20.44^{2}}$$

Multiply \frac{98596}{25} times \frac{4473}{4000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{98596\times 4473}{25\times 4000}}{20.44^{2}}$$

Do the multiplications in the fraction \frac{98596\times 4473}{25\times 4000}.

$$\frac{\frac{441019908}{100000}}{20.44^{2}}$$

Reduce the fraction \frac{441019908}{100000} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{110254977}{25000}}{20.44^{2}}$$

Calculate 20.44 to the power of 2 and get 417.7936.

$$\frac{\frac{110254977}{25000}}{417.7936}$$

Express \frac{\frac{110254977}{25000}}{417.7936} as a single fraction.

$$\frac{110254977}{25000\times 417.7936}$$

Multiply 25000 and 417.7936 to get 10444840.

$$\frac{110254977}{10444840}$$

Reduce the fraction \frac{110254977}{10444840} to lowest terms by extracting and canceling out 7.

$$\frac{15750711}{1492120}$$

Factor

$$\frac{71 \cdot 3 ^ {2} \cdot 157 ^ {2}}{5 \cdot 7 \cdot 2 ^ {3} \cdot 73 ^ {2}} = 10\frac{829511}{1492120} = 10.555927807414953$$