Q:

If $p^2$ is even then $p$ is even.

Let $p^2=6$. Is $\sqrt{6}$ even?
I believe $\sqrt{6}$ is not even an integer. Could you help me find the flaw in this statement. Thanks.

A:

"Even" and "odd" are properties of integers, not of arbitrary real numbers.  The correct statement is "if $p$ is an integer and $p^2$ is even, then $p$ is even."  
Someone might omit the "if $p$ is an integer" part if they think it is obvious from the context.  But apparently it was not obvious to you.

