What is the cube root of 1000?

1 Answer
Sep 25, 2016

Answer:

#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]}