Answer:
Real numbers are not closed under cube root
Step-by-step explanation:
The cube of each real number is increasing as the real numbers increases, giving a functional or one to one relationship. Therefore, the cube roots of real number have also a one to one relationship.
Given that a cube root of a number, ∛x = y therefore, y³ = x, we have that all real numbers, excluding zero, have one cube root, and two complex and conjugate roots
For the real number, 8, we have the cube roots given as follows;
∛8 = 2
Also, ∛8 = -1 + √3i and -1 - √3i
Given that not all cube roots of 8 are real numbers we have that real numbers are not closed under cube root.
