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June 30th, 2014, 12:33 AM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 431 Thanks: 18  square root of 6
Question: Prove that sqrt(6) is irrational NOTE: sqrt(6) = square root of 6 My attempt: (1) Let sqrt(6) = a/b a fraction in simplest form (2) so 6 = (a^2)/(b^2) (3) so 6(b^2) = a^2 (4) a^2 will have all prime factors raised to an even power (5) 6(b^2) will have prime factors 2 and 3 (2 x 3 = 6) raised to an odd power (6) (4) and (5) is impossible (7) Therefore, sqrt(6) = a/b is false ( 8 ) Therefore, sqrt(6) is irrational Is this correct? Is there another/better way? Thanks 
June 30th, 2014, 01:19 AM  #2 
Senior Member Joined: Apr 2014 From: Europa Posts: 584 Thanks: 177  

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