I have a theory that i need to prove but im not quite sure how to mathematically prove that it is true. Theory: When you square a rational number, each of the prime factors has an even exponent. For example, 10 --> If i square 10, which is a rational number, =10^2 =(5^2 x 2^2) --> both 5 and 2 are prime, and have even exponents. Thus, 10 is a rational number. √7 ? =(√7)^2 =7^1 --> odd exponent, thus irrational number. I want to prove this will work for any case. Any ideas??