Let's determine those decimal numbers whose square ends in 76.
The questionable numbers can only be 4 or 6, because only the squares of such numbers end in 6. The second last digit of a square number depends only on the last two digits of the base number. Therefore, in the case of 4, if the second last digit is $x$, its eightfold must end in $7-1=6$, and in the case of 6, $x$'s twelvefold must end in $7-3=4$. Both requirements are met by 2 and 7 in both cases.

Accordingly, the sought numbers are those in which after the hundreds,

$$
24,26,74,76
$$

follow.