Solve 1+1/4^2+1/5^2

$$1 + \frac { 1 } { 4 ^ { 2 } } + \frac { 1 } { 5 ^ { 2 } }$$

Evaluate

$$\frac{441}{400}=1.1025$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$1+\frac{1}{16}+\frac{1}{5^{2}}$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{16}{16}+\frac{1}{16}+\frac{1}{5^{2}}$$

Since \frac{16}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{16+1}{16}+\frac{1}{5^{2}}$$

Add 16 and 1 to get 17.

$$\frac{17}{16}+\frac{1}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{17}{16}+\frac{1}{25}$$

Least common multiple of 16 and 25 is 400. Convert \frac{17}{16} and \frac{1}{25} to fractions with denominator 400.

$$\frac{425}{400}+\frac{16}{400}$$

Since \frac{425}{400} and \frac{16}{400} have the same denominator, add them by adding their numerators.

$$\frac{425+16}{400}$$

Add 425 and 16 to get 441.

$$\frac{441}{400}$$

Factor

$$\frac{3 ^ {2} \cdot 7 ^ {2}}{2 ^ {4} \cdot 5 ^ {2}} = 1\frac{41}{400} = 1.1025$$