Tutorial 62
Squaring numbers between 3000 and 3099

  1. Choose a number between 3000 and 3099. (Start with numbers below 3025 to begin with, then graduate to larger numbers.)
  2. The first two digits are: 9 0 _ _ _ _ _
  3. The next two digits are 6 times the last two digits:
    9 0 X X _ _ _
  4. For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
    9 0 _ _ X X X

   Example:

  1. If the number to be squared is 3004:
  2. The first two digits are: 9 0 _ _ _ _ _
  3. The next two digits are 6 times the last two:
    6 × 4 = 24: _ _ 2 4 _ _ _
  4. For the last three digits, square the last two:
    4 × 4 = 16: _ _ _ _ 0 1 6
  5. So 3004 × 3004 = 9,024,016.

   See the pattern?

    For larger numbers, reverse the order:

  1. If the number to be squared is 3025:
  2. For the last three digits, square the last two:
    25 × 25 = 625: _ _ _ _ 6 2 5
  3. The middle two digits are 6 times the last two (keep the carry):
    6 × 25 = 150 (keep carry of 1): _ _ 5 0 _ _ _
  4. The first two digits are 90 + the carry:
    90 + 1 = 91: 9 1 _ _ _ _ _
  5. So 3025 × 3025 = 9,150,625.