To determine which of the given numbers are rational, let's analyze each option:
A. \( \sqrt{64} \) - The square root of 64 is 8, which is a whole number. Whole numbers are rational (can be expressed as a fraction, e.g., \( \frac{8}{1} \)). Therefore, this number is rational.
B. \( 0.145874… \) - This number seems to be a non-repeating decimal since it continues without a repeating pattern. Non-repeating decimals are not considered rational numbers. Therefore, this number is not rational.
C. \( 0.75 \) - This decimal can be expressed as the fraction \( \frac{75}{100} \), which simplifies to \( \frac{3}{4} \). Since it can be expressed as a fraction, this number is rational.
D. \( -8 \) - Negative eight is also a whole number and can be expressed as \( \frac{-8}{1} \). Therefore, this number is rational.
Based on this analysis, the rational numbers in the list are:
A. \( \sqrt{64} \), C. \( 0.75 \), and D. \( -8 \).