prove that √5 is irrational
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So, we get that 'p' and 'q' both have '5' as a common factor from equation (i) and (iv), but we supposed earlier that p and q are co-primes which have '1' as a common factor. So, it contradicts our assumption that pq supposed will not be a rational number. Hence, √5 is an irrational number.
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Well, to be perfectly honest in my humble opinion, of course without offending anyone who thinks different from my point of view but also by looking into this matter in a different perspective and without condemning one's view and by trying to make it objectified and considering each and everyone's valid opinion, I honestly believe that I completely forgot what I was going to say.
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