How to use the Fundamental Theorem of Arithmetic for a proof?

Question

How do you use the Fundamental Theorem of Arithmetic to prove that the sq. root of k is irrational for each positive integer k that is not a perfect square?

Answer 1

"Every integer greater than 1 either is prime itself or is the product of a unique combination of prime numbers."

 

The square root of a perfect square, then, would either be prime itself or the product of a unique combination of prime numbers. There also has to be at least two of every prime number in the prime factorization of a perfect square.