Which choices are real numbers? Check all that apply. A. (-16)^1/4

Which choices are real numbers? Check all that apply.

A. (-16)^1/4

B. (-4)^1/2

C. (-32)^1/5

D. (-8)^1/3

Answer: (-32)^1/5

Real numbers are those ones that can be represented as points on a number line. They comprise of rational numbers- fractions, integers and repeating decimals as well as irrational positive & negative numbers such as π and square roots of negative number. Options B and C are the main (imaginary) square roots and fifth root of negative values, with real numbers. On the other hand, option A – fourth root of a negative number does not equal to real. We are aware that an even-indexed root, such as square root or fourth root of negative, gives resultant imaginary numbers which does not have practical meaning on real line. On the other hand, option D has an unusual cube root that results into a real value when applied on negative. Then, -4 and – 32 raise to fractional exponents are both the members of real numbers whereas (-16)^1/4 does not; B and C satisfy these criteria for membership in real number system .