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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