Tutorial 45
Squaring numbers in the 30's

  1. Square the last digit (keep the carry)   _ _ _ X
  2. Multiply the last digit by 6, add the carry   _ _ X _
  3. The first digits will be 9 plus the carry:   X X _ _

   Example:

     If the number to be squared is 34:

  1. Square the last digit (keep the carry):
        4 × 4 = 16 (keep 1)     _ _ _ 6
  2. Multiply the last digit by 6, add the carry:
        6 × 4 = 24, 24 + 1 = 25    _ _ 5 _
  3. The first digits will be 4 plus the carry:
        9 (+ carry): 9 + 2 = 11  1 1 _ _
  4. So 34 × 34 = 1156.

   See the pattern?

     If the number to be squared is 36:

  1. Square the last digit (keep the carry):
        6 × 6 = 36 (keep 3)    _ _ _ 6
  2. Multiply the last digit by 6, add the carry:
        6 × 6 = 36, 36 + 3 = 39 (keep 3)  _ _ 9 _
  3. The first digits will be 9 plus the carry:
        9 (+ carry): 9 + 3 = 12  1 2 _ _.
  4. So 36 × 36 = 1296.

With some practice you will be giving these squares quickly.