|Jun13-11, 11:52 PM||#1|
Proof root N is irrational
I came across this question. How do you show that √N is irrational when N is a nonsquare integer?
|Jun14-11, 01:29 AM||#2|
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
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.
|Jun16-11, 07:12 AM||#3|
Nice. Thanks hammster143. Appreciate it.
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