Hi OldTimer
\((a+\sqrt b)(c+\sqrt d)\\ =ac+bd+a\sqrt d + c\sqrt b\\ \text{This will only be rational if, and only if, the last two terms cancel each other out ie}\\ a\sqrt d = -c\sqrt b\\ \text{which simplifies to}\\ \frac{c}{a}=-\frac{\sqrt d}{\sqrt b} \)
