Question

Observe the following pattern and find the missing digits. 
\(11^2\) = \(121\) 
\(101^2\) = \(10201\) 
\(1001^2 = 1002001\) 
\(100001^2 = 1…2…1 \)
\(10000001^2 = …\)

Answer 1

In the given pattern, it can be observed 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. 
Therefore,
\(100001^2 = 10000200001\)
\(10000001^2= 100000020000001\)