Tutorial 89
Squaring special numbers (9's and final 7)
  1. Choose a number with repeating 9's and a final 7.
  2. The square is made up of:
    • the same number of 9's as there are repeating 9's
    • 4
    • the same number of 0's as there are 9's in the square
    • A final 9

   Example:

  1. If the number to be squared is 9997:
  2. The square has:

    same number of 9's as there are
       repeating 9's:              9 9 9
        4                                4
    same number of 0's as 9's
       in the square                       0 0 0
    a final 9                                    9

  3. So 9997 × 9997 = 99940009.

   See the pattern?

  1. If the number to be squared is 999997:
  2. The square has:

    same number of 9's as there are
       repeating 9's:        9 9 9 9 9
        4                              4
    same number of 0's as 9's
       in the square                     0 0 0 0 0
    a final 9                                      9

  3. So 999997 × 999997 = 999994000009.