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
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What is $(-2)^3$? There's your answer. – HDE 226868 Dec 03 '14 at 01:46
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1you gotta use complex numbers – janmarqz Dec 03 '14 at 01:47
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Are you sure you haven't done something else wrong, causing you to think that the answer must be a cube root of 8 when it can actually be something else? – user2357112 Dec 03 '14 at 06:07
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$-2$ 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 $0.$)
Kevin Carlson
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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
Aditya Hase
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Whether it's "unfortunately" depends on what you want them for, I think. – David K Dec 03 '14 at 05:38