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Find a 5 digits Strobogrammatic numbers, so if we square it, the result is also a Strobogrammatic numbers.

We call a number Strobogrammatic if:

When it is typed on a calculator, and the calculator is spun 180 degrees, the number visually looks the same.

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Well, the smallest such number is

10001

because

$10001^2=100020001$

This also happens to be the only solution.

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If you want a cheeky answer:

00000^2 = 00000
because an infinite string of 0's is still 0, and 0 squared is 0

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