How do you simplify #root3(1000)#?

1 Answer
Apr 26, 2016

Answer:

#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]}