Reference: Elementary Number Theory, David M. Burton, Sixth Edition, Tata McGraw-Hill.
(We are all aware of the proof we learn in high school that is irrational. (due Pythagoras)). But, there is an interesting variation of that proof.
Let with , there must exist integers r and s such that . As a result, . This representation leads us to conclude that is an integer, an obvious impossibility. QED.