Is the square root of 3 a rational number

A rational number is any number that can be expressed as a/b, where a and b are integers.  Setting a/b equal to the square root of three and squaring, we have:

a^2/b^2=3

a^2=3b^2

However, because 3 is not a square number, three times a square cannot be another square.  So, there are no such a and b, and thus we have proven that the square root of three is not a rational number.