a) Using Remark 1.28, prove that the square root of an integer m is rational if and

Question:

a) Using Remark 1.28, prove that the square root of an integer m is rational if and only if m = k2 for some k ∈ N.
b) Prove that √n + 3 + √n is rational for some n ∈ N if and only if n = 1.
c) Find all n ∈ N such that √n + 1 + √n is rational.