Solve 2*2*3.14*3.14*30*30left(0.9232+0.17512/2right)/59.07^2

$$\frac{ 2 \cdot 2 \cdot 3.14 \cdot 3.14 \cdot 30 \times 30 \left( 0.9232+ \frac{ 0.17512 }{ 2 } \right) }{ { 59.07 }^{ 2 } }$$

Evaluate

$$\frac{4982844648}{484620125}\approx 10.281959809$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4\times 3.14\times 3.14\times 30\times 30\left(0.9232+\frac{0.17512}{2}\right)}{59.07^{2}}$$

Multiply 4 and 3.14 to get 12.56.

$$\frac{12.56\times 3.14\times 30\times 30\left(0.9232+\frac{0.17512}{2}\right)}{59.07^{2}}$$

Multiply 12.56 and 3.14 to get 39.4384.

$$\frac{39.4384\times 30\times 30\left(0.9232+\frac{0.17512}{2}\right)}{59.07^{2}}$$

Multiply 39.4384 and 30 to get 1183.152.

$$\frac{1183.152\times 30\left(0.9232+\frac{0.17512}{2}\right)}{59.07^{2}}$$

Multiply 1183.152 and 30 to get 35494.56.

$$\frac{35494.56\left(0.9232+\frac{0.17512}{2}\right)}{59.07^{2}}$$

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

$$\frac{35494.56\left(0.9232+\frac{17512}{200000}\right)}{59.07^{2}}$$

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

$$\frac{35494.56\left(0.9232+\frac{2189}{25000}\right)}{59.07^{2}}$$

Convert decimal number 0.9232 to fraction \frac{9232}{10000}. Reduce the fraction \frac{9232}{10000} to lowest terms by extracting and canceling out 16.

$$\frac{35494.56\left(\frac{577}{625}+\frac{2189}{25000}\right)}{59.07^{2}}$$

Least common multiple of 625 and 25000 is 25000. Convert \frac{577}{625} and \frac{2189}{25000} to fractions with denominator 25000.

$$\frac{35494.56\left(\frac{23080}{25000}+\frac{2189}{25000}\right)}{59.07^{2}}$$

Since \frac{23080}{25000} and \frac{2189}{25000} have the same denominator, add them by adding their numerators.

$$\frac{35494.56\times \frac{23080+2189}{25000}}{59.07^{2}}$$

Add 23080 and 2189 to get 25269.

$$\frac{35494.56\times \frac{25269}{25000}}{59.07^{2}}$$

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.

$$\frac{\frac{887364}{25}\times \frac{25269}{25000}}{59.07^{2}}$$

Multiply \frac{887364}{25} times \frac{25269}{25000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{887364\times 25269}{25\times 25000}}{59.07^{2}}$$

Do the multiplications in the fraction \frac{887364\times 25269}{25\times 25000}.

$$\frac{\frac{22422800916}{625000}}{59.07^{2}}$$

Reduce the fraction \frac{22422800916}{625000} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{5605700229}{156250}}{59.07^{2}}$$

Calculate 59.07 to the power of 2 and get 3489.2649.

$$\frac{\frac{5605700229}{156250}}{3489.2649}$$

Express \frac{\frac{5605700229}{156250}}{3489.2649} as a single fraction.

$$\frac{5605700229}{156250\times 3489.2649}$$

Multiply 156250 and 3489.2649 to get 545197640.625.

$$\frac{5605700229}{545197640.625}$$

Expand \frac{5605700229}{545197640.625} by multiplying both numerator and the denominator by 1000.

$$\frac{5605700229000}{545197640625}$$

Reduce the fraction \frac{5605700229000}{545197640625} to lowest terms by extracting and canceling out 1125.

$$\frac{4982844648}{484620125}$$

Factor

$$\frac{3 \cdot 8423 \cdot 2 ^ {3} \cdot 157 ^ {2}}{5 ^ {3} \cdot 11 ^ {2} \cdot 179 ^ {2}} = 10\frac{136643398}{484620125} = 10.281959809242343$$