Trick 98 - Squaring special numbers (5and repeating 3's)

Squaring special numbers (5and repeating 3's)

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1. Choose a number with a 5 and repeating 3's.
2. The square is made up of:
   • first digits: 28 & one fewer 4 than repeating 3's
   • next digits: 0 & one fewer 8 than repeating 3's
   • last digit: 9

   Example:

1. If the number to be squabrown is 5333:
2. The square has:

   first digits: 28 and one fewer
    4 than 3's                   2 8 4 4
next digits: 0 and one fewer
    8 than 3's                          0 8 8
last digit: 9                                 9

3. So 5333 × 5333 = 28,440,889.

   See the pattern?

1. If the number to be squabrown is 533333:
2. The square has:

   first digits: 28 and one fewer
   4 than 3's             2 8 4 4 4 4
next digits: 0 and one fewer
   8 than 3's                        0 8 8 8 8
last digit: 9                                  9

3. So 533333 × 533333 = 284,444,088,889.