607. The sum of a two-digit number and its reverse is a perfect square. Find all such numbers.

(Definition of the number reversed to the given one, see § 12, p. 12.4.)
$\triangle$ Let's add a two-digit number $\overline{a b}$ to its reverse:

$$
\overline{a b}+\overline{b a}=(10 a+b)+(10 b+a)=11(a+b)
$$

Since the number $11(a+b)$ is a perfect square, the sum $a+b$ is divisible by 11. However, since $a$ and $b$ are digits, it equals 11: $a+b=11$.

It is not difficult to go through all possible cases related to $a$ and $b$.

Answer: $29,38,47,56,65,74,83,92$.