Subject 1. Determine the natural numbers $\overline{a b}$ that satisfy the relation $\sqrt{a+\sqrt{\overline{a b}}}=a$.
## Subject 1.

|  | $\sqrt{a+\sqrt{a b}}=a \Leftrightarrow \sqrt{\overline{a b}}=a^{2}-a$ |
| :--- | :--- | :--- |
| $a^{2}-a$ is a natural number $\Rightarrow \overline{a b}$ is a perfect square | 1p |
| Possible cases are studied and $\overline{a b}=36$ is obtained | 2p |