Solve (5/2)^2-(73/40)^2

$$( \frac { 5 } { 2 } ) ^ { 2 } - ( \frac { 73 } { 40 } ) ^ { 2 }$$

Evaluate

$$\frac{4671}{1600}=2.919375$$

Solution Steps

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{25}{4}-\left(\frac{73}{40}\right)^{2}$$

Calculate \frac{73}{40} to the power of 2 and get \frac{5329}{1600}.

$$\frac{25}{4}-\frac{5329}{1600}$$

Least common multiple of 4 and 1600 is 1600. Convert \frac{25}{4} and \frac{5329}{1600} to fractions with denominator 1600.

$$\frac{10000}{1600}-\frac{5329}{1600}$$

Since \frac{10000}{1600} and \frac{5329}{1600} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10000-5329}{1600}$$

Subtract 5329 from 10000 to get 4671.

$$\frac{4671}{1600}$$

Factor

$$\frac{3 ^ {3} \cdot 173}{2 ^ {6} \cdot 5 ^ {2}} = 2\frac{1471}{1600} = 2.919375$$