Proof that Square Root of Two is Irrational Number

To proof that square root of two is irrational number, we assuming that square root of two is rational number, that is square root of two equals a over b where a and b as integer prime. So a equals b times square root of two or a square equals two times b square. Because a square is two times an integer number, so a square is integer, so that a is integer too. And than we assuming that a is two times c, so the equation is four times c square equals two times b square or two times c square equals b square. So that b square is integer and b is integer too. But it is impossible because a and b is impossible to integer because they are relative prime number. So assumption that square root of two is rational number has brought us to the impossibility and must be annulled. And it is proofed that square root of two is irrationals number.