Question

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

Answer 1

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