Introductory reference on rationality and irrationality of real numbers

Question

I am looking for a good reference on the proof of the rationality or the irrationality of some real numbers.

I think these kinds of problems show a nice variety of proofs and techniques, ranging from arithmetic (Euclid's proof of the irrationality of $\sqrt{2}$, criteria to determine whether $\frac{\ln(a)}{\ln(b)}$ is rational or not (for $a,b$ integers),...) to calculus (irrationality of $\pi$ or $e$,...), passing through algebra (Rational Root Test to prove the irrationality of $n^{th}$ roots of integers,...).

I am not looking for a survey of the state of the art, but an introduction to these problems.

Answer 1

I highly recommend Ivan Niven's monographs

1. Numbers: Rational and Irrational, and
2. Irrational Numbers.

They are both excellent introductions to the topics that you have mentioned you want to study.