8、On a birthday card printed with April 29, a child erased two positive integers $x, y$ between 4 and 29, resulting in a five-digit number $\overline{4 x y 29}$, and found that it 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
Answer: 223.
Solution: Since $40000<\overline{4 x y 29}<50625$, and $40000=200^{2}, 50625=225^{2}$, it follows that $200<T<225$. Also, because the last digit of $T^{2}=\overline{4 x y 29}$ is 9, the last digit of $T$ must be 3 or 7. Between 200 and 225, there are 5 such numbers: $203, 207, 213, 217, 223$. By calculation, only $223^{2}=49729$, so $T=223$. (The corresponding date is February 23).