Does the period length $l(pq)$ of the continued fraction of $\sqrt{pq}$, for $p$ and $q$ primes, follow some type of divisibility property, say $$ l(pq) = c\frac{l(p)}{l(q)} \quad\text{or}\quad c\frac{l(q)}{l(p)}, $$ where $l(p)$ is the period of $\sqrt{p}$ and $c > 0$ is an absolute constant.

In the previous question, Franz Lemmermeyer mentioned that it depends on the squarefree kernel of the integer.

Note: The theorem on the upper bound of the length of period of continued fraction implies that $l(\ \cdot\ )$ is not multiplicative.

Thank you, Jerald Jetson.