- #1
mccalli1
- 5
- 0
I have a theory that i need to prove but I am 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??
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??