Assignment:
Suppose that k∈N is not a perfect nth power, i.e K is not equal to mn,m, n ∈ N
(a) Prove that n√k is not a member of Q, the set of all rational numbers.
(b) Infer that the nth root of a natural number is either a natural number or it is irrational.
Provide complete and step by step solution for the question and show calculations and use formulas.