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 n∈N 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;
m2−1 for any m>2.
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