How to find continued fraction of the form $a\sqrt{b}$?

Question

For the form $\sqrt{b}$, I could just apply the recursive quadratic formula: $$P_{k+1} = a_kQ_k - P_k$$ $$Q_{k+1} = \dfrac{d - P^2_{k+1}}{Q_k}$$ $$\alpha_k = \dfrac{P_k + \sqrt{d}}{Q_k}$$ $$a_k = \lfloor \alpha_k \rfloor$$

In this case, we have a coefficient namely $a$, so what's $d$? Is it still $b$?

Thanks,

Answer 1

(So you can have something to "accept"...)

$a \sqrt{b} = \sqrt{a^2b}$ - Chan