You can
put this solution on YOUR website! A man was born in the first half of the nineteenth century was x years old in the year x^2 when he was born ?
That means he was born between 1800 and 1850.
The square root of 1850 is 43.01162634, so the last year that was a square
before 1850 was 432 or 1849. So he was 43 years old in 1849.
So he must have been born 43 years earier in 1849-43 = 1806.
[Incidentally anybody who was or will be 35 years old in some part of 2015
will be 45 in the year 452. That will be 10 years from now in 2025.]
Edwin