Final answer:
Rational numbers are those that can be expressed as a fraction of two integers. From the given options, −5/4, −8.68, and 16 are rational numbers because they fulfill this criterion. Option A, the square root of 24, is not rational because it cannot be expressed as a fraction with an integer numerator and a non-zero integer denominator.
Step-by-step explanation:
To determine which numbers are rational from the given options, you need to understand that a rational number is any number that can be expressed as the quotient or fraction
of two integers, with a numerator p and a non-zero denominator q. Integers, finite decimals, and repeating decimals are all examples of rational numbers.
- 24−−√ (Option A) is not rational because it is the square root of 24, which is not a perfect square and thus does not result in a finite or repeating decimal.
- −5/4 (Option B) is rational because it can be expressed as a fraction of two integers.
- −8.68 (Option C) is rational because it is a finite decimal.
- 16 (Option D) is also rational because it is an integer and all integers are rational numbers as they can be expressed as the ratio of themselves to 1.
Therefore, from the given options, B, C, and D are rational numbers.