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As a continuation of the reply by Benjamin, Let me give some references and give more information.

Both Theorems appear in the book "Continued Fractions" By Andrew Mansfield Rockett and Peter Sz├╝sz. The first is Theorem 3 on page 45, and the second is a remark before Theorem 1 on page 50. The second is not stated correctly (there should not be any coeffiecient before the square root):

Theorem(Lagrange Estimate): Let $t= \frac{P_0+\sqrt{D}}{Q_0}$ with $D$ not a perfect square and $P_0,Q_0$ are integers. Then the length of the period of $t$ is at most $2D$.

A better asymptotics is given by the following (which is Theorem 1 of page 50):

Theorem: Let $t$ be as above with the addtional assumption that $Q_0$ divide $D-P_0^2$. Then if $L(t)$ denoted the length of the period of $t$ then $$L(t)=O(\sqrt{D}log(D))$$

I'm not sure what the constant is (it is related to the divisor function)... I didn't read the proof yet!