If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and S is the set of irrational numbers, list the set(s)for which a solution to the given equation exists. If a solution to the given equation does not belong to any set, state none.
-$$x ^ { 3 } = 3$$
A) $R$
B) I, Q, R
C) $Q , R$
D) $S , R$

Question

Quizplus · Accepted Answer

The equation $x^3 = 3$ has a solution that is not a rational number, integer, or natural number, but it is a real number. Since it's not rational, it must be irrational. Therefore, the solution belongs to the set of irrational numbers (S) and the set of real numbers (R).

If R Is the Set of Real Numbers, Q Is x3=3x ^ { 3 } = 3x3=3

If R Is the Set of Real Numbers, Q Is $x ^ { 3 } = 3$