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Real Analysis of Powers and Roots

Please see the attached file for the fully formatted problems.

Suppose that is not a perfect nth power, i.e K is not equal to

(a) Prove that 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.

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Real analysis problems are solved. The solution is detailed and well-presented.

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