Solve {left(0.05/391.01right)}^2+9{left(0.02/3.97right)}^2

$${ \left( \frac{ 0.05 }{ 391.01 } \right) }^{ 2 } +9 { \left( \frac{ 0.02 }{ 3.97 } \right) }^{ 2 }$$

Evaluate

$$\frac{55043915461}{240966540471409}\approx 0.00022843$$

Solution Steps

Expand \frac{0.05}{391.01} by multiplying both numerator and the denominator by 100.

$$\left(\frac{5}{39101}\right)^{2}+9\times \left(\frac{0.02}{3.97}\right)^{2}$$

Calculate \frac{5}{39101} to the power of 2 and get \frac{25}{1528888201}.

$$\frac{25}{1528888201}+9\times \left(\frac{0.02}{3.97}\right)^{2}$$

Expand \frac{0.02}{3.97} by multiplying both numerator and the denominator by 100.

$$\frac{25}{1528888201}+9\times \left(\frac{2}{397}\right)^{2}$$

Calculate \frac{2}{397} to the power of 2 and get \frac{4}{157609}.

$$\frac{25}{1528888201}+9\times \frac{4}{157609}$$

Multiply 9 and \frac{4}{157609} to get \frac{36}{157609}.

$$\frac{25}{1528888201}+\frac{36}{157609}$$

Add \frac{25}{1528888201} and \frac{36}{157609} to get \frac{55043915461}{240966540471409}.

$$\frac{55043915461}{240966540471409}$$

Factor

$$\frac{1861 \cdot 29577601}{61 ^ {2} \cdot 397 ^ {2} \cdot 641 ^ {2}} = 0.00022842970378093234$$