Tuesday, 4 December 2012

How can I find a non-prime number whose square root is irrational?



I already know that when n is prime, that n is irrational (this is true in every case), but I know that this isn't only true for primes, 8 is irrational, but it's not a prime number.



So how could I find numbers like these, where it's square root is an irrational number, but yet it's not prime?


Answer




Hint: if nN is not a perfect square, then n is irrational.



[ EDIT ]    Examples of such non-prime n whose square root is irrational:


  • any non-prime integer whose prime factorization includes a prime at an odd power;


  • m! for any m>2;


  • m21 for any m>2.



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