# What is the cube root of 1000?

Sep 25, 2016

$10$

#### Explanation:

$1000 = 10 \times 10 \times 10 = {10}^{3}$

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 $y = \sqrt[3]{x}$ 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]}