
#1
Jun1311, 11:52 PM

P: 5

I came across this question. How do you show that √N is irrational when N is a nonsquare integer?
Cheers. 



#2
Jun1411, 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 N=A^2/B^2 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. 



#3
Jun1611, 07:12 AM

P: 5

Nice. Thanks hammster143. Appreciate it.
bgwyh_88 


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