Let's categorize each of the given numbers into their appropriate subsets of the real numbers:
A. 15
- Natural Numbers: Yes, 15 is a natural number.
- Whole Numbers: Yes, whole numbers include all natural numbers and zero.
- Integers: Yes, integers include all whole numbers and their negative counterparts.
- Rational Numbers: Yes, 15 can be expressed as a fraction (e.g., 15/1).
So, 15 belongs to the subsets: Natural numbers, Whole numbers, Integers, Rational numbers.
B. -1.4583
- Natural Numbers: No, it is negative.
- Whole Numbers: No, it is negative.
- Integers: No, it is not a whole number or a non-negative integer.
- Rational Numbers: Yes, -1.4583 is a rational number because it can be expressed as a fraction (-14583/10000), and it is a terminating decimal.
So, -1.4583 belongs to the subset: Rational numbers.
C. 57 squared
- 57 squared equals \( 57^2 = 3249 \).
- Natural Numbers: Yes, it is positive.
- Whole Numbers: Yes, it is a whole number.
- Integers: Yes, it is an integer.
- Rational Numbers: Yes, it can be expressed as a fraction (e.g., 3249/1).
- Irrational Numbers: No, 3249 is a perfect square (it is the square of 57), thus it is not an irrational number.
So, 57 squared (3249) belongs to the subsets: Natural numbers, Whole numbers, Integers, Rational numbers.
To summarize:
- A. 15: Natural numbers, Whole numbers, Integers, Rational numbers.
- B. -1.4583: Rational numbers.
- C. 57 squared (3249): Natural numbers, Whole numbers, Integers, Rational numbers.