Check out Prime number - Prime elements in rings - Wikipedia.
The wording of 'positive prime numbers named "d" that are in Z and meet the condition that the quadratic integers in Q[Sqrt(d)] are in the form of a+b*Sqrt(d) , where of course a and b must be rational' doesn't make much sense. The quadratic integers in Q[sqrt(d)] will be a subset of Q[sqrt(d)], and wouldn't be characterized by saying a and b rational, which characterizes Q[sqrt(d)]. Also, your sentence has the setup "A meets the condition that B" where B is essentially unrelated to A. Please check the wording.
Of course if 'a' and 'b' are both even then we can get rid of that 2 in the denominator and proceed from there. What book are you using, by the way?