Show that {Q( square root of 13,+,*} is a field?
Let Q( square root of 13 ={x+y square root of 13 where x,y are elements of Q}

Q of course is rational numbers
Addition and multiplication are defined as follows
(a+b square root of 13)+(c+d square root of 13) =(a+c)+(b+d) square root of 13
(a+b square root of 13)(c+d square root of 13) = (ac+13bd)+(ad+bc) square root of 13

Show that {Q( square root of 13,+,*} is a field