Tutorial 50
Squaring numbers in the 80's

  1. Square the last digit (keep the carry)   _ _ X
  2. Multiply the last digit by 16, add the carry   _ X _
  3. The first digits will be 64 plus the carry:  X X _ _

   Example:

     If the number to be squared is 83:

  1. Square the last digit:
        3 × 3 = 9    _ _ _ 9
  2. Multiply the last digit by 16:
        16 × 3 = 30 + 18 = 48    _ _ 8 _
  3. The first digits will be 64 plus the carry:
        64 (+ carry): 64 + 4 = 68  6 8 _ _
  4. So 83 × 83 = 6889.

   See the pattern?

     If the number to be squared is 86:

  1. Square the last digit (keep the carry):
        6 × 6 = 36 (keep 3)    _ _ _ 6
  2. Multiply the last digit by 16, add the carry:
        16 × 6 = 60 + 36 = 96 96 + 3 = 99 (keep 9)  _ _ 9 _
  3. The first digits will be 64 plus the carry:
        64 (+ carry): 64 + 9 = 73  7 3 _ _
  4. So 86 × 86 = 7396.