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November 15th, 2010, 05:32 PM  #1 
Member Joined: Nov 2010 Posts: 78 Thanks: 0  Uniqueness of Square Root proof
Given any r which is an element of the positive rational numbers, the number root(r) is uniquein the sense that, if x is a positive real number such that x^2 = r, then x = root(r). I know that in order to prove uniqueness, one needs to show that if x^2 = r = y^2 where x and y are elements from the positive rationals, then x = y. But I am not sure how to go about doing this. Any help would be appreciated! 
November 15th, 2010, 05:52 PM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Uniqueness of Square Root proof
Try x^2=y^2 x^2y^2=0 (x+y)(xy)=0 so x = y or x =y since Q is a field. But since they are both positives, x =y is excluded. 
November 16th, 2010, 12:19 PM  #3 
Member Joined: Nov 2010 Posts: 78 Thanks: 0  Re: Uniqueness of Square Root proof
Thank you! This should do the trick.


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