Some Different Ways to Prove The Irrationality of The Square Root of 2

In this talk, we will explore the different ways to prove the irrationality of the square root of 2. First, we will consider the classical proof that is often shown in a math classroom. Then, we will consider several other proofs of the same result. For each of these other proofs, we will investigate the extent to which they generalize to prove the irrationality of the square root of 3, the square root of p, the n-th root of p (where p is a prime) and more.