the smallest non-palidronic number whose square is a palindrome.
To find the smallest non-palindromic number whose square is a palindrome, we need to follow a systematic approach. Here's how you can proceed:
1. Start by considering the smallest non-palindromic number, which is 10.
2. Square the number: 10 * 10 = 100.
3. Check if the square is a palindrome. In this case, 100 is not a palindrome.
4. Increment the number by 1.
5. Repeat steps 2-4 until you find a square that is a palindrome.
- For example, you can try 11 next: 11 * 11 = 121, which is a palindrome.
- However, since we are looking for the smallest non-palindromic number, we need to continue iterating.
6. Continue incrementing the number and checking if its square is a palindrome until we find the smallest one.
- For example, let's try 12: 12 * 12 = 144, not a palindrome.
- Next, we try 13: 13 * 13 = 169, not a palindrome.
- We keep incrementing until we find a palindrome:
- 17 * 17 = 289, not a palindrome.
- 18 * 18 = 324, not a palindrome.
- 19 * 19 = 361, not a palindrome.
- 20 * 20 = 400, not a palindrome.
- 21 * 21 = 441, a palindrome!
Therefore, the smallest non-palindromic number whose square is a palindrome is 21.