Solve (4000*0.0157)^2/4000^2+476476^2

$$\frac { ( 4000 \times 0.0157 ) ^ { 2 } } { 4000 ^ { 2 } + 476476 ^ { 2 } }$$

Evaluate

$$\frac{24649}{1419033616100}\approx 0.000000017$$

Solution Steps

Multiply 4000 and 0.0157 to get 62.8.

$$\frac{62.8^{2}}{4000^{2}+476476^{2}}$$

Calculate 62.8 to the power of 2 and get 3943.84.

$$\frac{3943.84}{4000^{2}+476476^{2}}$$

Calculate 4000 to the power of 2 and get 16000000.

$$\frac{3943.84}{16000000+476476^{2}}$$

Calculate 476476 to the power of 2 and get 227029378576.

$$\frac{3943.84}{16000000+227029378576}$$

Add 16000000 and 227029378576 to get 227045378576.

$$\frac{3943.84}{227045378576}$$

Expand \frac{3943.84}{227045378576} by multiplying both numerator and the denominator by 100.

$$\frac{394384}{22704537857600}$$

Reduce the fraction \frac{394384}{22704537857600} to lowest terms by extracting and canceling out 16.

$$\frac{24649}{1419033616100}$$

Factor

$$\frac{157 ^ {2}}{349 \cdot 2797 \cdot 14537 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 1.737027207836278 \times 10^{-8}$$