Observe the following pattern and find $10000001^{2}$
$11^{2} = 121$
$101^{2} = 10201$
$1001^{2} = 1002001$
$10000001^{2} = . . . . . . . . . . . . . .$

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Solution

The square of the number with zeroes in between two $1^{'} s$ has the same number of zeroes in between $1$ and $2$ and between $2$ and $1$ , in its square.
So, $100001^{2} = 10000200001$
$10000001^{2} = 100000020000001$

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Similar questions

11^{2} = 121

101^{2} = 10201

1001^{2} = 1002001

100001^{2} = 10000200001

10000001^{2} = . . . . . . . . . . .

11^{2} = 121

101^{2} = 10201

1001^{2} = 1002001

100001^{2} = 1

2

1

10000001^{2} =

101^{2} = 10201

1001^{2} = 1002001

10001^{2} =_________

11^{2} = 121

101^{2} = 10201

10101^{2} = 102030201

1010101^{2} = . . . . . . . . . . . . . . . . . . . . . .

11^{2} = 121

101^{2} = 10201

10101^{2} = 102030201

1010101^{2} = . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . .^{2} = 10203040504030201

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