How do you simplify root3(1000)?

1 Answer
Apr 26, 2016

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]}