8. On a birthday card printed with April 29, a child added two positive integers $x$ and $y$ between 4 and 29, resulting in a five-digit number $\overline{4 x y 29}$. It turns out that this number is exactly the square of the positive integer $T$ corresponding to their birthday: $\overline{4 x y 29}=T^{2}$. Then the number $T$ corresponding to the child's birthday is $T=$ $\qquad$
8. 223 .

From $200^{2}=40000<\overline{4 x y 29}<50625=225^{2}$, we know $200<T<225$.
Also, since the last digit of $T^{2}=\overline{4 x y 29}$ is 9, the last digit of $T$ is 3 or 7.

Notice that, between 200 and 225, there are 5 such numbers: 203, 207, 213, 217, 223.
Upon verification, only $223^{2}=49729$.
Therefore, the corresponding date is February 23.