Which Choices Are Real Numbers? Check All That Apply
In mathematics, a real number is a number that can be represented on the real number line. Real numbers include all rational numbers, irrational numbers, and complex numbers.
The question "Which choices are real numbers? Check all that apply" is a common math problem that can be used to test a student’s understanding of real numbers. The problem typically presents a list of expressions, and the student must determine which expressions evaluate to real numbers.
To solve this type of problem, it is important to remember the following rules about real numbers:
- The square root of a positive number is always real.
- The square root of a negative number is always imaginary.
- The cube root of a positive number is always real.
- The cube root of a negative number is always imaginary.
With these rules in mind, we can solve the following problems:
Problem 1
(-16)^(1/4) The base of this expression is negative, so the answer is imaginary. The correct answer is none.
Problem 2
(-4)^(1/2) The base of this expression is negative, so the answer is imaginary. The correct answer is none.
Problem 3
(-32)^(1/5) The base of this expression is negative, but the exponent is odd, so the answer is real. The correct answer is (-32)^(1/5).
Problem 4
(-8)^(1/3) The base of this expression is negative, but the exponent is odd, so the answer is real. The correct answer is (-8)^(1/3).
Additional Questions
Here are some additional questions that can be used to test a student’s understanding of real numbers:
- Which of the following expressions evaluate to real numbers?
- (-16)^(1/3)
- (-4)^(1/4)
- (-32)^(1/6)
- (-8)^(1/2)
- Which of the following expressions evaluate to imaginary numbers?
- (-16)^(1/2)
- (-4)^(1/3)
- (-32)^(1/4)
- (-8)^(1/6)
By answering these questions, students can test their understanding of the rules for real numbers.
