A prime number between 10 and 50 remains unchanged when its digits are reversed to form a two digit number again. The square of this two digit prime number is equal to which of the following values?

Introduction / Context:
This question combines basic number theory with place value understanding. You are asked to find a two digit prime number between 10 and 50 that remains the same when its digits are reversed, and then compute its square. Such a number is a palindromic prime in the two digit range. Once the number is identified, squaring it is straightforward arithmetic.

Given Data / Assumptions:
- The number is a prime number. - It lies strictly between 10 and 50. - Reversing its digits yields the same number, so it is a two digit palindrome. - We must find the square of this number and match it with the given options.

Concept / Approach:
A two digit number that remains unchanged when its digits are reversed must have the same tens and units digit, so it is of the form 11, 22, 33, 44 and so on. Within the interval 10 to 50, such palindromes are 11, 22, 33 and 44. Among these, we need the one that is prime. A prime number has exactly two positive divisors, 1 and itself. We test each candidate for primality and then compute the square of the correct one.

Step-by-Step Solution:
Step 1: List two digit palindromes between 10 and 50: 11, 22, 33 and 44. Step 2: Check primality of 11. It is divisible only by 1 and 11, so it is prime. Step 3: Check 22. It is divisible by 2 and 11, so it is composite. Step 4: Check 33. It is divisible by 3 and 11, so it is composite. Step 5: Check 44. It is divisible by 2 and 11, so it is composite. Step 6: Therefore, 11 is the only two digit palindromic prime between 10 and 50. Step 7: Compute its square: 11 * 11 = 121.

Verification / Alternative check:
You can confirm the squaring operation by using distributive multiplication. Think of 11 as 10 + 1. Then 11^2 = (10 + 1) * (10 + 1) = 10 * 10 + 2 * 10 * 1 + 1 * 1 = 100 + 20 + 1 = 121. This quick mental check confirms that the square of 11 is indeed 121. No other two digit palindrome in the given range is prime, so the result is unique.

Why Other Options Are Wrong:
- 484 is 22^2, but 22 is not prime. - 1089 is 33^2, and 33 is composite. - 1936 is 44^2, and 44 is composite. - 729 is 27^2 or 3^6, and 27 is not the required palindromic prime. These values do not correspond to the square of a palindromic prime between 10 and 50.

Common Pitfalls:
Some students mistakenly consider any prime between 10 and 50, without ensuring that it is a palindrome. Others miscompute squares in a hurry, especially when dealing with mental calculations. It is also easy to overlook the fact that 11 is both prime and palindromic. Listing all palindromes in the range first, and then checking primality, is the safest method.

Final Answer:
The square of the two digit palindromic prime between 10 and 50 is 121.