Cube roots answers

Question

So I am in a middle of a problem and I got stuck at cube root of $8$. I know the answer is is $2$ but my book is showing a positive and negative 2. I thought that cube roots had only one answer. Please confirm which one would be correct and thanks

Answer 1

$-2$ isn't a cube root of $8$. If you're sure your book's claiming it is, then that's a typo. You're right that numbers only have one cube root, as long as we're sticking to real numbers. If you allow imaginary numbers, they have three (except for $0.$)

Answer 2

No, $-2$ is not cube root of $8$,

You can try $$(-2)(-2)(-2)=(4)(-2)=-8\neq8$$

And ,$$x^3=8$$ $$x^3-8=0$$ $$(x-2)(x^2+2x+4)=0$$

$$x=2,-1\pm i\sqrt3$$

As $x^3-8=0$ is a cubic polynomial it has 3 roots out of which two are unfortunately complex