Final answer:
The rational numbers from the options given are √64 (8), which is rational as it can be expressed as 8/1, 4 (an integer, which can be written as 4/1), and 2 (also an integer, expressible as 2/1). The status of 3.56967... as rational or irrational depends on whether the decimals repeat in a pattern.
Step-by-step explanation:
The student asked which numbers are rational. Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero. Here are the evaluations:
- A. √64 is equal to 8, which can be written as 8/1, so it is a rational number.
- B. 4 is an integer, and all integers are rational since they can be expressed as a ratio of themselves to 1, like 4/1.
- C. 2 is also an integer and can be expressed as 2/1, making it a rational number.
- D. 3.56967... if the dots indicate a non-repeating decimal, then it would not be a rational number. But if the decimals repeat in a pattern, it could be rational. Since the pattern of repetition is not specified, we cannot conclude decisively without more information. Typically, non-terminating, non-repeating decimals are irrational.
Therefore, the rational numbers from the given options are √64 (A), 4 (B), and 2 (C).