Tutorial 57
Squaring numbers in the 700's

  1. Choose a number in the 700s (practice with smaller numbers, then progress to larger ones).
  2. Square the last two digits (keep the carry): _ _ _ _ X X
  3. Multiply the last two digits by 14 and
    add the carry: _ _ X X _ _
  4. The first two digits will be 49 plus the carry: X X _ _ _ _

   Example:

  1. If the number to be squared is 704:
  2. Square the last two digits (keep the carry):
    4 × 4 = 16: _ _ _ _ 1 6
  3. Multiply the last two digits by 14 and
    add the carry: 14 × 4 = 56: _ _ 5 6 _ _
  4. The first two digits will be 49 plus the carry: 4 9 _ _ _ _
  5. So 704 × 704 = 495,616.

   See the pattern?

  1. If the number to be squared is 725:
  2. Square the last two digits (keep the carry):
    25 × 25 = 625: _ _ _ _ 2 5
  3. Multiply the last two digits by 14 and
    add the carry: 14 × 25 = 10 × 25 + 4 × 25
    = 250 + 100 = 350. 350 + 6 = 356: 56: _ _ 5 6 _ _
  4. The first two digits will be 49 plus the carry: 49 + 3 = 52: 5 2 _ _ _ _
  5. So 725 × 725 = 525,625.