My Math Forum Uniqueness of Square Root proof

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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^2-y^2=0 (x+y)(x-y)=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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Uniqueness of the square root

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