As we know, $1$, $4$, $9$, $16$ are square numbers. $10^{8}=\left (10^{4}\right )^{2}$, so, the next one is $\left (10^{4}+1\right )^{2}$. 
There is a sequence of squares of some natural numbers: $1$, $4$, $9$, $16$, $\cdots$ One of the numbers in this sequence is $10^{8}$. What is the next number after $10^{8}$? ($2001$ Math Kangaroo Problem, Level $$11$$-$$12$$, Question \#$14$) 

[1] $\left (10^{4}+1\right )^{2}$ 
[2] $\left (10^{8}+1\right )^{2}$ 
[3] $\left (10^{5}\right )^{2}$ 
[4] $\left (10^{8}\right )^{2}$ 
[5] $\left (10^{4}\right )^{2}+1$ 