Saturday, September 7, 2019

elementary number theory - Square root of a prime is irrational

How can one prove that the square root of a prime number (e.g. 61) is irrational.


First we need to prove that 61 is prime. This can be done by simply showing that 49<61<64 and so 7<61<8 then the only possible prime factors of 61 are 2,3,5,7. Then by contradictions and DIC we can show that 61 is prime.


Now how can we show that 61 is irrational?

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