Answer :

According to this given pattern, we can observe that the squares of the given numbers have the same number of zeroes before and after the digit 2 as it was in the original number.

Hence,

We can see that with every term, the number of zeroes that are in the square of the number, are in the solution with that many zeroes left and right of 2.100001^{2} = 10000200001

10000001^{2} = 100000020000001

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