A palindromic number is one which when expressed in base $10$ with no leading zeros, reads the same left to right and right to left. For example, $44944$ is a (base 10) palindrome.
I can find quite a few palindromes which are also perfect squares; indeed there are an infinite set of them of the form $1,121,10201,1002001, \ldots$. In each of these cases, however, the square root of the palindrome is itself a palindrome.
I would like to know about palindromes which are the square of non-palindromes:
Are there any perfect square palindromes whose square roots are not palindromic?
Is there an infinite set of perfect square palindromes whose square roots are not palindromic?
Are the answers to these questions different in other bases?
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