Question

What is the cube root of 1000?

Answer 1

`10`

Explanation:

`1000 = 10xx10xx10 = 10^3`

In other words `10` cubed is `1000`

So `10` is a cube root of `1000`

Any Real number has exactly one Real cube root. Any non-zero Real number has two other cube roots which are Complex numbers.

The graph of `y = x^3` looks like this:

graph{x^3 [-10, 10, -5, 5]}

Notice that any horizontal line will intersect this curve at exactly one point. The `x` coordinate of the point of intersection is the Real cube root of the `y` coordinate.

The graph of `y = root(3)(x)` is formed by reflecting the above graph in the diagonal line `y=x` (thereby swapping `x` and `y`) and looks like this:

graph{root(3)(x) [-10, 10, -5, 5]}