In the section on irrationality of sqrt 2 it is shown that sqrt(n^2+1) and sqrt(n^2-1) are irrational with n any integer greater than 1. I think the arguement applies equally to any rational greater than 1. Does it follow that the ratio sqrt(n^2-1)/sqrt(n^2+1) is also irrational ? Also does the proof hold for roots other than square eg cube roots, fourth roots etc ?
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