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Cube Roots - Concept
A square root is an exponent of one-half. A cube root is an exponent of one-third. Square roots of negative numbers do not have real number roots since the product of any real number and itself is positive. Cube roots do exist for negative numbers since the product of three negatives is a negative. Cube roots re-appear often in Geometry and in Algebra II.
In your Algebra class, you're going to deal with square roots a lot but there's other types of roots that aren't just square roots. There's cube roots and there's fourth roots and fifth roots, stuff like that. So I'm just going to show you guys a little bit about what a cube root is.
First thing is notation. Notation's how we write it. This is how you would write the cubed root of x and what it means is a number whose cube is x. If that doesn't make sense to you listen carefully to this. This means what number times itself three times is equal to x. Be careful. It doesn't mean what number times 3 gives you x. It's what number times itself three times gives you x.
Like here's an example. The cubed root of 8. That means what number times itself 3 times gives you the answer 8. It's not what number times 3 is 8. Well the number that's times itself 3 times is 8 is 2 because 2 to the third power is 8. Think about it, 2 times 2 is 4 times 2 again is 8. That's how I'd write it. The same process goes with fourth roots.
You probable won't see this in your Algebra class but I bet it's going to show up sometime thereafter. The fourth root of 81. That means what number times itself 4 times gives you 81 and the answer is 3 because 3 times 3 is 9 times 3 again is 27 times 3 again is 81. So when you see these little bitty tiny numbers outside a square root sign, what that's telling you is it's not a square root anymore, it's turned into a cubed root or a fourth root. It's going to show up sometime in your Algebra class, but not very often. Just beware of it when you see it. This is what it means.