Tutorial 65
Squaring numbers between 6000 and 6099

  1. Choose a number between 6000 and 6099.
  2. The first three digits are: 3 6 0 _ _ _ _ _
  3. The next two digits are 12 times the last two digits:
    _ _ _ X X _ _
  4. For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
    _ _ _ _ _ X X X

   Example:

  1. If the number to be squared is 6004:
  2. The first three digits are: 3 6 0 _ _ _ _ _
  3. The next two digits are 12 times the last two:
    12 × 4 = 48: _ _ _ 4 8 _ _ _
  4. For the last three digits, square the last two:
    4 × 4 = 16: _ _ _ _ 0 1 6
  5. So 6004 × 6004 = 36,048,016.

   See the pattern?

    For numbers greater than 6008, reverse the order:

  1. If the number to be squared is 6020:
  2. For the last three digits, square the last two:
    20 × 20 = 400: _ _ _ _ 4 0 0
  3. The middle two digits are 12 times the last two:
    12 × 20 = 240 (keep carry): _ _ _ 4 0 _ _ _
  4. The first digits are 360 + the carry:
    360 + 2 = 362: 3 6 2 _ _ _ _ _
  5. So 3025 × 3025 = 36,240,400.