University of Isfahan Mathematics and Society 2345-6493 4 2 2019 08 23 On proofs of the lrrationality of the square root of 2 On proofs of the lrrationality of the square root of 2 25 45 24279 10.22108/msci.2019.119712.1345 FA Seyed Mohammad Amin Khatami Department of Computer Science, Birjand University of Technology, Birjand, Iran Ghasem Khakshoor Department of Basic Sciences, Birjand Girls' Technical and Vocational School, Technical and Vocational University, Birjand, Iran Journal Article 2019 10 18 This article reviews some of the most famous proofs of the irrationality of the square root of 2. Given the nature of defining irrational numbers, we will see that most proofs (except Proof No. 23) have been done either directly or indirectly using proof by contradiction. We have tried to mention cases that have the potential to be generalized to a proof for the irrationality of the square root of other numbers as well. Some proofs have been slightly modified to ensure clarity of the resulting text. Additionally, some new results have been obtained in certain cases. This article reviews some of the most famous proofs of the irrationality of the square root of 2. Given the nature of defining irrational numbers, we will see that most proofs (except Proof No. 23) have been done either directly or indirectly using proof by contradiction. We have tried to mention cases that have the potential to be generalized to a proof for the irrationality of the square root of other numbers as well. Some proofs have been slightly modified to ensure clarity of the resulting text. Additionally, some new results have been obtained in certain cases. https://math-sci.ui.ac.ir/article_24279_55ca45e00515bb75d7cd8c94db25109b.pdf