Squaring special numbers (9’s and final 1)

Follow the following Steps:

  1. Choose a number with repeating 9’s and a final 1.
  2. The square is made up of:
    • one fewer 9 than there are repeating 9’s
    • 82
    • the same number of 0’s as there are 9’s in the square
    • A final 81

  Example-1:

  1. If the number to be squared is 9991:
  2. The square has:One fewer 9 than the
       repeating 9's:        9 9
    82                           8 2
    same number of 0's as 9's
       in the square                 0 0
    a final 81                            8 1
  3. So 9991 × 9991 = 99820081.

   Example-2:

  1. If the number to be squared is 999991:
  2. The square has:one fewer 9 than the
       repeating 9's:       9 9 9 9
    82                              8 2
    same number of 0's as 9's
       in the square                    0 0 0 0
    a final 81                                  8 1
  3. So 999991 × 999991 = 999982000081