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June 30th, 2014, 12:33 AM   #1
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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
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June 30th, 2014, 01:19 AM   #2
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proofsfromthebook.com/2012/12/23/square-root-of-6-is-irrational/

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