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I was doing a number problem as homework about proving that the square root of all integer non perfect squares are irrational. I have proven that it is true for all primes, using Euler’s lemma. However I am not sure how to approach this problem for all integer non perfect squares. Any help or solution would be appreciated very much! Thank you so much!

1937874
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  • Sorry, I want to know how to prove it’s irrational not whether it must be either integer or irrational number. – 1937874 Mar 11 '24 at 11:32
  • The Rational Root Theorem or the method of infinite descent can be used to prove any integer that isn't a perfect square has an irrational square root. – Nate Mar 11 '24 at 11:33
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    Please do not repost the exact same question which was closed as a duplicate. The answer to your question is there. It’s integer when it’s root of perfect square. Irrational otherwise. – Aig Mar 11 '24 at 11:34

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