Solve (1331/1000)^2-(1/1331)^2

$$( \frac { 1331 } { 1000 } ) ^ { 2 } - ( \frac { 1 } { 1331 } ) ^ { 2 }$$

Evaluate

$$\frac{3138427376721}{1771561000000}\approx 1.771560436$$

Solution Steps

Calculate \frac{1331}{1000} to the power of 2 and get \frac{1771561}{1000000}.

$$\frac{1771561}{1000000}-\left(\frac{1}{1331}\right)^{2}$$

Calculate \frac{1}{1331} to the power of 2 and get \frac{1}{1771561}.

$$\frac{1771561}{1000000}-\frac{1}{1771561}$$

Least common multiple of 1000000 and 1771561 is 1771561000000. Convert \frac{1771561}{1000000} and \frac{1}{1771561} to fractions with denominator 1771561000000.

$$\frac{3138428376721}{1771561000000}-\frac{1000000}{1771561000000}$$

Since \frac{3138428376721}{1771561000000} and \frac{1000000}{1771561000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3138428376721-1000000}{1771561000000}$$

Subtract 1000000 from 3138428376721 to get 3138427376721.

$$\frac{3138427376721}{1771561000000}$$

Factor

$$\frac{3 ^ {2} \cdot 7 \cdot 13 \cdot 37 \cdot 131 \cdot 409 \cdot 1933}{2 ^ {6} \cdot 5 ^ {6} \cdot 11 ^ {6}} = 1\frac{1366866376721}{1771561000000} = 1.77156043552607$$