Question

Observe the following pattern and find the missing numbers.

${11}^2=121$

${101}^2=10201$

${1001}^2=1002001$

${100001}^2=1\_\_\_\_2\_\_\_\_1$

${10000001}^2=\_\_\_\_\_\_\_\_\_$

Answer 1

From 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.

Also, the number starts and end with $1$.

Now for the given number

${100001}^2=1\_\_\_\_2\_\_\_\_1$

The given number consist $4$ zeroes.

Therefore, square of the number will consist $4$ zeroes left to the $2$ and $4$ zeroes to the right of $2$.

${100001}^2=10000200001$

Similarly

${10000001}^2=\_\_\_\_\_\_\_\_\_$

This number consist $6$ zeroes.

Therefore, square of the number will consist $6$ zeroes left to the $2$ and $6$ zeroes to the right of $2$.

${10000001}^2=100000020000001$

Hence, the missing numbers are ${100001}^2=10000200001$ and ${10000001}^2=100000020000001$