Question

Question

Describe all the sets and subsets the number 64−−√ belongs to and enter the number corresponding to the correct answer as your response.

Answer 1

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.