Let a be an integer. Prove that a^2 is divisible by 5 if and only if a is divisible by 5. Now use that result to prove that there does not exist a rational number whose square is 5.
Last edited by padsinseven; Oct 31st 2007 at 08:15 AM. Reason: more to add
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Originally Posted by padsinseven Let a be an integer. Prove that a^2 is divisible by 5 if and only if a is divisible by 5. Now use that result to prove that there does not exist a rational number whose square is 5. Say then . But we are told that with thus a contradiction.
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