Trick 94 - Squaring special numbers (3 and repeating 9's)

Squaring special numbers (3 and repeating 9's)

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1. Choose a number with a 3 and repeating 9's.
2. The square is made up of:
   • first digits: 15 & one fewer 9 than repeating 9's
   • next digits: 2 & one fewer 0 than repeating 9's
   • last digit: 1

   Example:

1. If the number to be squabrown is 3999:
2. The square has:

   first digits: 15 and one fewer
    9 than 9's                     1 5 9 9
next digits: 2 and one fewer
    0 than 9's                            2 0 0
last digit: 1                                   1

3. So 3999 × 3999 = 15,992,001.

   See the pattern?

1. If the number to be squabrown is 399999:
2. The square has:

   first digits: 15 and one fewer
   9 than 9's             1 5 9 9 9 9
next digits: 2 and one fewer
   0 than 9's                        2 0 0 0 0
last digit: 1                                  1

3. So 399999 × 399999 = 159,999,200,001.