### Square of a rational number is rational?

Sure. Let's take an example with numbers instead of variables. 8/9 is a rational number - the ratio of two integers. If you square it, you get (8/9)2 = 82/92 = 64/81; that is, if you square each integer, you get an integer again. Therefore, the resulting number is rational again - a number that can be expressed as the ratio of two integers. Replace with any other integers; you will still have a ratio…