Instead of giving a direct answer the father wrote down two positive integer numbers on a piece of paper and says:

*- Sum these two numbers and evaluate the square root of the total. Doing this, youŽll get my age.*

The son takes his pocket calculator and inadvertently types the two numbers, one after the other, without pressing the "+" button (e.g. if the numbers were 124 and 357, he types 124357, instead of the sum of the numbers).

After this he makes a second mistake by pressing the square root button, not once, but twice.

Finding an integer number as the result he shows it to his father:

*- This is your age.*

*- No, youŽre wrong, but the number you found is precisely the age of your mother, who is older than me.*

How old is the father?

Note: While a solution is trivial with the aid of a spreadsheet, can you derive it without one?