Question
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−−√ belongs to several sets and subsets.
1. Real Numbers: This is the set of all numbers that can be represented on the number line. The number 64−−√ belongs to this set as it is a real number.
2. Rational Numbers: This set includes all numbers that can be expressed as a fraction of two integers. The number 64−−√ is not a rational number since it is an irrational number.
3. Irrational Numbers: This set includes all numbers that cannot be expressed as a fraction of two integers. The number 64−−√ belongs to this set as it is an irrational number.
4. Algebraic Numbers: This set includes all numbers that are solutions to algebraic equations with integer coefficients. The number 64−−√ is an algebraic number since it is the solution to the equation x^2 - 64 = 0.
5. Real Numbers (except zero): This is a subset of the real numbers that excludes zero. The number 64−−√ belongs to this subset.
6. Positive Real Numbers: This is a subset of the real numbers that includes only positive numbers. The number 64−−√ belongs to this subset.
7. Natural Numbers: This set includes all positive integers. The number 64−−√ is not a natural number since it is not an integer.
8. Whole Numbers: This set includes all non-negative integers. The number 64−−√ is not a whole number since it is not an integer.
9. Integers: This set includes all positive and negative whole numbers and zero. The number 64−−√ is not an integer since it is not a whole number.
Based on the given information, the number 64−−√ belongs to the following sets and subsets: Real Numbers, Irrational Numbers, Algebraic Numbers, Real Numbers (except zero), Positive Real Numbers.
The correct answer is 59910.
To determine the sets and subsets the number 64 √ belongs to, let's consider the following options:
1. Natural numbers (N): This set includes all positive integers (1, 2, 3, ...) but does not include 0 or negative numbers. Since √64 is equal to 8, which is a positive integer, 64 √ belongs to the natural numbers. The correct answer number for this option is 1.
2. Whole numbers (W): This set includes all natural numbers (0, 1, 2, 3, ...) but also includes 0. Since √64 is equal to 8, which is a whole number, 64 √ belongs to the whole numbers. The correct answer number for this option is 2.
3. Integers (Z): This set includes all whole numbers (..., -3, -2, -1, 0, 1, 2, 3, ...) and their negatives. Since √64 is equal to 8, which is an integer, 64 √ belongs to the integers. The correct answer number for this option is 3.
4. Rational numbers (Q): This set includes all numbers that can be expressed as a ratio of two integers. Since √64 can be expressed as 8/1, which is a ratio of integers, 64 √ belongs to the rational numbers. The correct answer number for this option is 4.
5. Irrational numbers (I): This set includes all numbers that cannot be expressed as a ratio of two integers. Since √64 is equal to 8, which is a rational number, 64 √ does not belong to the irrational numbers. The correct answer number for this option is 5.
So, the correct answer would be the numbers corresponding to the sets the number 64 √ belongs to. Based on the descriptions above, the correct response would be:
1, 2, 3, and 4.