Palindromic Squares with Non-Palindromic Roots

Theorem

$676, 69 \, 696, 94 \, 249, 698 \, 896, 5 \, 221 \, 225, 6 \, 948 \, 496, 522 \, 808 \, 225, \ldots$

The sequence of those corresponding non-palindromic square roots begins:

$26, 264, 307, 836, 2285, 2636, 22 \, 865, 24 \, 846, 30 \, 693, \ldots$

By investigating all square numbers which are palindromic.

$\ds 676$

$=$

$\ds 26^2$

$\ds 69 \, 696$

$=$

$\ds 264^2$

$\ds 94 \, 249$

$=$

$\ds 307^2$

$\ds 698 \, 896$

$=$

$\ds 836^2$

$\ds 5 \, 221 \, 225$

$=$

$\ds 2285^2$

$\ds 6 \, 948 \, 496$

$=$

$\ds 2636^2$

$\ds 522 \, 808 \, 225$

$=$

$\ds 22 \, 865^2$

and so on.

$\blacksquare$