To determine if the sum of two rational numbers, \( \sqrt{25} \) and \( \frac{1}{8} \), is a rational number, we first evaluate \( \sqrt{25} \):
\[ \sqrt{25} = 5 \]
Now we add \( 5 \) and \( \frac{1}{8} \):
\[ 5 + \frac{1}{8} = \frac{5 \cdot 8}{8} + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{40 + 1}{8} = \frac{41}{8} \]
Since \( \frac{41}{8} \) is in the form of a fraction where both the numerator (41) and denominator (8) are integers and the denominator is not zero, \( \frac{41}{8} \) is a rational number.
Thus, the sum of \( \sqrt{25} \) and \( \frac{1}{8} \) is a rational number because both components of the sum are rational, and the sum of any rational numbers is also rational.