Question

How do you simplify `root3(1000)`?

Answer 1

`root(3)(1000) = 10`

Explanation:

Note that `1000 = 10xx10xx10 = 10^3`

So: `root(3)(1000) = root(3)(10^3) = 10`

As a function from Real numbers to Real numbers, `f(x) = x^3` is one-to-one with domain and range the whole of `RR`.

So the Real cube root `f^(-1)(y) = root(3)(y)` is also a well-defined one-to-one function with domain and range the whole of `RR`.

graph{(x^3 - y)(y^3-x) = 0 [-10, 10, -5, 5]}