A good answer might be:

When oldGuess*oldGuess is very close to N.

Ending Condition for the Loop

When oldGuess*oldGuess is very close to N, then 

N/(oldGuess*oldGuess) == almost 1.00

or 

N/(oldGuess*oldGuess) - 1.00 == almost 0.00

Unfortunately, we don't know if "almost 0.00" will be negative or positive, so we need to take the absolute value of it to make sure that it is positive. So the loop will end when: 

|N/(oldGuess*oldGuess) - 1.00| == almost 0.00

Now we need to decide what "almost 0.00" means. If the variables are all of type double precision, then they will have about 15 decimal places of precision. To be safe, assume that 14 places of precision can be reached. "Almost zero" to 14 places of precision means "less than .00000000000001"

QUESTION 13:

What is .00000000000001 in scientific notation?