Solve (25/4)^2+(25/3)^2

$$( \frac { 25 } { 4 } ) ^ { 2 } + ( \frac { 25 } { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{15625}{144}\approx 108.506944444$$

Solution Steps

Calculate \frac{25}{4} to the power of 2 and get \frac{625}{16}.

$$\frac{625}{16}+\left(\frac{25}{3}\right)^{2}$$

Calculate \frac{25}{3} to the power of 2 and get \frac{625}{9}.

$$\frac{625}{16}+\frac{625}{9}$$

Least common multiple of 16 and 9 is 144. Convert \frac{625}{16} and \frac{625}{9} to fractions with denominator 144.

$$\frac{5625}{144}+\frac{10000}{144}$$

Since \frac{5625}{144} and \frac{10000}{144} have the same denominator, add them by adding their numerators.

$$\frac{5625+10000}{144}$$

Add 5625 and 10000 to get 15625.

$$\frac{15625}{144}$$

Factor

$$\frac{5 ^ {6}}{2 ^ {4} \cdot 3 ^ {2}} = 108\frac{73}{144} = 108.50694444444444$$