Squaring special numbers (1 and repeating 9’s)

Follow the following Steps:

  1. Choose a number with a 1 and repeating 9’s.
  2. The square is made up of:
    • first digits: 3 & one fewer 9 than repeating 9’s
    • next digits: 6 & one fewer 0 than repeating 9’s
    • last digit: 1

   Example-1:

  1. If the number to be squared is 1999:
  2. The square has:first digits: 3 and one fewer
        9 than 9's                      3 9 9
    next digits: 6 and one fewer
        0 than 9's                            6 0 0
    last digit: 1                                   1
  3. So 1999 × 1999 = 3996001.

Example-2:

  1. If the number to be squared is 199999:
  2. The square has:first digits: 3 and one fewer
       9 than 9's                 3 9 9 9 9
    next digits: 6 and one fewer
        0 than 9's      &                   6 0 0 0 0
    last digit: 1                                     1
  3. So 199999 × 199999 = 39999600001.