Proof root N is irrational

by bgwyh_88
Tags: irrational, proof, root
bgwyh_88 is offline
Jun13-11, 11:52 PM
P: 5
I came across this question. How do you show that √N is irrational when N is a nonsquare integer?

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hamster143 is offline
Jun14-11, 01:29 AM
P: 986
It depends on what you're allowed to use.

But the simplest way would be to use the fundamental theorem of arithmetic (that every integer has a unique prime factorization). For any N, if sqrt(N) is rational, you can write that as


and therefore

B^2 N = A^2

and it's not hard to get from that + the fundamental theorem to the conclusion that N is a square.
bgwyh_88 is offline
Jun16-11, 07:12 AM
P: 5
Nice. Thanks hammster143. Appreciate it.


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