Rule

This trick is to find square of a number containing all 9s.
Let n be the number of 9s.

Step 1:
Write 9 (n - 1) times (leftmost) then write 8, then write 0 (n - 1) times and finally wirte 1 (right most).

Example

999^2
There are three 9s. So, n = 3.
Write 9 two times(n - 1 = 2).
Then, write 8.
Then, write 0 two times(n - 1 = 2).
finally write 1.
So, the answer is 998001.

99999^2
There are five 9s. So, n = 5.
Write 9 four times(n - 1 = 4).
Then, write 8.
Then, write 0 four times(n - 1 = 4)..
finally write 1.
So, the answer is 9999800001.