Describe all the sets and subsets the number 64−−√
belongs to and enter the number corresponding to the correct answer as your response.
The number √64 can belong to the following sets and subsets:
1. Set of natural numbers (N)
- The square root of 64 is equal to 8, which is a natural number.
2. Set of whole numbers (W)
- The square root of 64 is equal to 8, which is a whole number.
3. Set of integers (Z)
- The square root of 64 is equal to 8, which is an integer.
4. Set of rational numbers (Q)
- The square root of 64 is equal to 8, which can also be expressed as the fraction 8/1. Therefore, it is a rational number.
5. Set of real numbers (R)
- The square root of 64 is equal to 8, which is a real number.
None of the above
By examining the options, we can see that the correct answer is (5) Set of real numbers (R).
(W)8
To determine the sets and subsets that the number √64 belongs to, we need to understand the properties of the number and its classification.
1. Real Numbers: The number √64 is a real number because it can be expressed on the number line without any imaginary or complex components.
2. Rational Numbers: A rational number can be expressed as a fraction of two integers. The number √64 can be written as 8/1 or 8, which means it is a rational number.
3. Integers: Integers are whole numbers without any fractional or decimal parts. Since √64 is an integer, it belongs to the set of integers.
4. Natural Numbers: Natural numbers are positive integers starting from 1. Since √64 is positive and an integer, it is a natural number.
5. Whole Numbers: Whole numbers are non-negative integers including zero. Since √64 is non-negative and an integer, it is a whole number.
Based on the properties described above, √64 belongs to all of the sets mentioned (1, 2, 3, 4, and 5). Therefore, the correct answer would be 12345.
To determine the sets and subsets the number 64√ belongs to, we need to consider various number systems and number sets.
1. Natural Numbers (N): These are the counting numbers 1, 2, 3, and so on. Since 64√ is not a natural number (as it is not a whole number), it does not belong to this set.
2. Whole Numbers (W): These include all the natural numbers along with zero (0). As 64√ is not a whole number, it does not belong to this set either.
3. Integers (Z): This set includes all positive and negative whole numbers along with zero (0). Again, 64√ is not an integer, so it does not belong to this set.
4. Rational Numbers (Q): Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers, and q is not equal to zero. Since the square root of 64 is 8 (a whole number), 64√ can be expressed as the fraction 8/1. Therefore, it belongs to the set of rational numbers.
5. Real Numbers (R): Real numbers include rational numbers, irrational numbers, and the number zero. As 64√ is a real number (since it can be expressed as 8/1), it belongs to this set.
6. Irrational Numbers (I): Irrational numbers are real numbers that cannot be expressed as a fraction p/q, where p and q are integers. As 64√ is a rational number (since it can be expressed as 8/1), it does not belong to the set of irrational numbers.
Based on the above explanations, the number 64√ belongs to the sets of rational numbers (Q) and real numbers (R).
Please choose the number corresponding to the correct answer:
1. Natural Numbers (N)
2. Whole Numbers (W)
3. Integers (Z)
4. Rational Numbers (Q)
5. Real Numbers (R)
6. Irrational Numbers (I)
Your response should be either 4 or 5, depending on the classification you are looking for.