That would be 26 . . . its square is 676.
There are two smaller palindromic squares . . . 121 and 484 ... but they're the squares of
11 and 22 respectively, which are palindromic, so they flunk the question's specifications.
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262 = 676
11
121
11 is a palindrome.11 squared (i.e., 11 times 11) is 121, which is also a palindrome.
4, which is the square of the prime number 2, is the smallest composite number.