Solve (25/8)^2+2.5^2

$$( \frac { 25 } { 8 } ) ^ { 2 } + 2.5 ^ { 2 }$$

Evaluate

$$16.015625$$

Solution Steps

Calculate \frac{25}{8} to the power of 2 and get \frac{625}{64}.

$$\frac{625}{64}+2.5^{2}$$

Calculate 2.5 to the power of 2 and get 6.25.

$$\frac{625}{64}+6.25$$

Convert decimal number 6.25 to fraction \frac{625}{100}. Reduce the fraction \frac{625}{100} to lowest terms by extracting and canceling out 25.

$$\frac{625}{64}+\frac{25}{4}$$

Least common multiple of 64 and 4 is 64. Convert \frac{625}{64} and \frac{25}{4} to fractions with denominator 64.

$$\frac{625}{64}+\frac{400}{64}$$

Since \frac{625}{64} and \frac{400}{64} have the same denominator, add them by adding their numerators.

$$\frac{625+400}{64}$$

Add 625 and 400 to get 1025.

$$\frac{1025}{64}$$

Factor

$$\frac{41 \cdot 5 ^ {2}}{2 ^ {6}} = 16\frac{1}{64} = 16.015625$$