My Math Forum N-th Root Irrationality Proof

 Number Theory Number Theory Math Forum

 May 5th, 2011, 10:34 AM #1 Member   Joined: Nov 2010 Posts: 78 Thanks: 0 N-th Root Irrationality Proof Hey all, any help with the following proof would be appreciated: The real number n-th root of 2 is irrational. A similar proof, which says that the square root of 2 is irrational, is proved in the following way by contradiction: Assume sqroot(2) = m/n for some m,n in Z (integers) Since it is rational, you can assume m and n have no common factors. 2 = m^2 / n^2 implies m / n = 2n / m This means n divides m, but that means sqroot(2) is an integer, which is a contradiction. At our disposal, we have the fact that: -The real numbers sqroot(2) is irrational -If r in the Naturals is not a perfect square, then sqroot(r) is irrational -Let m and n be nonzero integers. Then (m/n)*sqroot(2) is irrational Thanks for the help!
 May 5th, 2011, 04:18 PM #2 Global Moderator   Joined: May 2007 Posts: 6,661 Thanks: 648 Re: N-th Root Irrationality Proof The proof for nth root is essentially the same as for square root. Assume k/m is nth root, with the fraction in lowest terms, so that k or m (or both) has to be odd. Then k^n=2m^n. Therefore k is even, then m is even and the original fraction was not lowest terms.

 Tags irrationality, nth, proof, root

,

,

### nth root of an irrational

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post rain Abstract Algebra 14 May 6th, 2013 06:18 AM FreaKariDunk Real Analysis 4 October 24th, 2012 12:45 PM Eureka Number Theory 10 October 27th, 2011 06:47 PM clandarkfire Algebra 4 May 14th, 2011 10:06 PM jstarks4444 Number Theory 11 February 17th, 2011 04:48 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top