1. The problem statement, all variables and given/known data Prove that for any n, sqrt n + sqrt (n+1) is irrational. 2. Relevant equations 3. The attempt at a solution Well, I know that sqrt 2 + sqrt 3 is irrational. How about sqrt n + sqrt (n+1)? Let sqrt n + sqrt (n+1) be rational. [sqrt n + sqrt (n+1)]^2 = (m^2/n^2) n + (n+1)^2 + 2 sqrt(n^2 + n) = (m^2/n^2) n + (n+1)^2 is rational. Then, I don't know how to continue... I read from a book that to prove the sqrt of a composite number is irrational, we should use one method. Then if we were to prove the sqrt of a prime number is irrational, we should use another method. Then I read from another website that in Real Analsysis, there are many approaches to solve a problem. I take this Introductory Analysis this semester. This course is so different from the other maths courses. Does memorising all of the axioms help in this case? Since all the proof need them. Thanks.