Final answer:
The prime number that fits the criteria is 5. Its square is greater than 10, less than 100, and it is not a factor of 21.
Step-by-step explanation:
Considering the criteria given for the number, we are looking for a prime number whose square is greater than 10 and less than 100, and it should not be a factor of 21. Starting with the smallest prime number greater than the square root of 10, which is 4, we find that 5 is the next prime number. Squaring 5 gives us 25, which satisfies the condition of being less than 100. However, moving to the next prime number, 7, and squaring it gives us 49. This still meets our criteria. The next prime number is 11, whose square is 121, which exceeds our limit of 100. Therefore, we must consider 5 and 7. Since 7 is a factor of 21, we can eliminate it, leaving us with 5 as the correct prime number that fits all conditions.