The answer to exercise marked [BB] can be found in the Back of the Book.(a) [BB] Use the r...

The answer to exercise marked [BB] can be found in the Back of the Book.

(a) [BB] Use the result of Problem 23 to prove that is irrational; that is, show that it is impossible to write for integers a, b. [Hint: Without loss of generality, assume that a and b have no common factors other than ±1. Why is there no loss of generality?]

(b) Let n be a natural number, n ≡ 2 (mod 3). Use Problem 23 to prove that is irrational.