Solve 2*2*3.14*3.14*30*30left(1.0184+0.17512/2right)/62.05^2

$$\frac{ 2 \cdot 2 \cdot 3.14 \cdot 3.14 \cdot 30 \times 30 \left( 1.0184+ \frac{ 0.17512 }{ 2 } \right) }{ { 62.05 }^{ 2 } }$$

Evaluate

$$\frac{49069454472}{4812753125}\approx 10.195714012$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4\times 3.14\times 3.14\times 30\times 30\left(1.0184+\frac{0.17512}{2}\right)}{62.05^{2}}$$

Multiply 4 and 3.14 to get 12.56.

$$\frac{12.56\times 3.14\times 30\times 30\left(1.0184+\frac{0.17512}{2}\right)}{62.05^{2}}$$

Multiply 12.56 and 3.14 to get 39.4384.

$$\frac{39.4384\times 30\times 30\left(1.0184+\frac{0.17512}{2}\right)}{62.05^{2}}$$

Multiply 39.4384 and 30 to get 1183.152.

$$\frac{1183.152\times 30\left(1.0184+\frac{0.17512}{2}\right)}{62.05^{2}}$$

Multiply 1183.152 and 30 to get 35494.56.

$$\frac{35494.56\left(1.0184+\frac{0.17512}{2}\right)}{62.05^{2}}$$

Expand \frac{0.17512}{2} by multiplying both numerator and the denominator by 100000.

$$\frac{35494.56\left(1.0184+\frac{17512}{200000}\right)}{62.05^{2}}$$

Reduce the fraction \frac{17512}{200000} to lowest terms by extracting and canceling out 8.

$$\frac{35494.56\left(1.0184+\frac{2189}{25000}\right)}{62.05^{2}}$$

Convert decimal number 1.0184 to fraction \frac{10184}{10000}. Reduce the fraction \frac{10184}{10000} to lowest terms by extracting and canceling out 8.

$$\frac{35494.56\left(\frac{1273}{1250}+\frac{2189}{25000}\right)}{62.05^{2}}$$

Least common multiple of 1250 and 25000 is 25000. Convert \frac{1273}{1250} and \frac{2189}{25000} to fractions with denominator 25000.

$$\frac{35494.56\left(\frac{25460}{25000}+\frac{2189}{25000}\right)}{62.05^{2}}$$

Since \frac{25460}{25000} and \frac{2189}{25000} have the same denominator, add them by adding their numerators.

$$\frac{35494.56\times \frac{25460+2189}{25000}}{62.05^{2}}$$

Add 25460 and 2189 to get 27649.

$$\frac{35494.56\times \frac{27649}{25000}}{62.05^{2}}$$

Convert decimal number 35494.56 to fraction \frac{3549456}{100}. Reduce the fraction \frac{3549456}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{887364}{25}\times \frac{27649}{25000}}{62.05^{2}}$$

Multiply \frac{887364}{25} times \frac{27649}{25000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{887364\times 27649}{25\times 25000}}{62.05^{2}}$$

Do the multiplications in the fraction \frac{887364\times 27649}{25\times 25000}.

$$\frac{\frac{24534727236}{625000}}{62.05^{2}}$$

Reduce the fraction \frac{24534727236}{625000} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{6133681809}{156250}}{62.05^{2}}$$

Calculate 62.05 to the power of 2 and get 3850.2025.

$$\frac{\frac{6133681809}{156250}}{3850.2025}$$

Express \frac{\frac{6133681809}{156250}}{3850.2025} as a single fraction.

$$\frac{6133681809}{156250\times 3850.2025}$$

Multiply 156250 and 3850.2025 to get 601594140.625.

$$\frac{6133681809}{601594140.625}$$

Expand \frac{6133681809}{601594140.625} by multiplying both numerator and the denominator by 1000.

$$\frac{6133681809000}{601594140625}$$

Reduce the fraction \frac{6133681809000}{601594140625} to lowest terms by extracting and canceling out 125.

$$\frac{49069454472}{4812753125}$$

Factor

$$\frac{43 \cdot 643 \cdot 2 ^ {3} \cdot 3 ^ {2} \cdot 157 ^ {2}}{5 ^ {5} \cdot 17 ^ {2} \cdot 73 ^ {2}} = 10\frac{941923222}{4812753125} = 10.195714011821456$$