Tutorial 86
Squaring special numbers (9's and final 4)

  1. Choose a number with repeating 9's and a final 4.
  2. The square is made up of:
    • one fewer 9 than there are repeating 9's
    • 88
    • the same number of 0's as there are 9's in the square
    • A final 36

   Example:

  1. If the number to be squared is 9994:
  2. The square has:

    one fewer 9 than the
       repeating 9's:        9 9
    88                           8 8
    same number of 0's as 9's
       in the square                 0 0
    a final 36                           3 6

  3. So 9994 × 9994 = 99880036.

   See the pattern?

  1. If the number to be squared is 999994:
  2. The square has:

    one fewer 9 than the
       repeating 9's:   9 9 9 9
    88                          8 8
    same number of 0's as 9's
       in the square                0 0 0 0
    a final 36                              3 6

  3. So 999994 × 999994 = 999988000036.