My grandfather was X years old in the year X squared. In which year was he born?
For example if he was 33 years old in the year 1089 AD (= 33 x 33), he would have been born in 1056 AD - but then of course he would currently be nearly a thousand years old! You can safely assume that none of my family had children when they were very, very old, and I'm not too old myself.
A good starting point would be to find the age he would have to be if we were talking about 2010, and 2010 = 44.8 x 44.8 (approx). So our first guess is aged 44 in 1936 (= 44 x 44), which means he was born in 1892.
Just to double check the next possible age. He could have been aged 43 in 1849 (= 43 x 43) and born in 1806, which was over 200 years ago, and the question said that he didn't have children as a very old man.