Question

Assuming that the square root of 2 is rational and is = to an even number divided by an odd number.2 multiplied by the odd number squared is= to the even number squared

Answer 1

It is not clear what your question is, but perhaps you are trying to prove that sqrt2 is irrational. If you assume it is a ratio of two integers reduced to lowest terms (and therefore rational), you get a contradiction.

For a proof, see

http://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php