Squaring a 2-digit number ending in 4

1. Take a 2-digit number ending in 4.
2. Square the 4; the last digit is 6: _ _ _ 6
   (keep carry, 1.)
3. Multiply the first digit by 8 and add the carry (1);
   the 2nd number will be the next to the last digit:
   _ _ X 6 (keep carry).
4. Square the first digit and add the carry: X X _ _.

   Example:

1. If the number is 34, 4 x 4 = 16 (keep carry, 1);
   the last digit is _ _ _ 6.
2. 8 x 3 = 24 (multiply the first digit by 8), 24 + 1 = 25
   (add the carry):
   the next digit is 5: _ _ 5 6. (Keep carry, 2.)
3. Square the first digit and add the carry, 2: 1 1 5 6.
4. So 34 x 34 = 1156.

   See the pattern?

1. For 84 x 84, 4 x 4 = 16 (keep carry, 1);
   the last digit is _ _ _ 6.
2. 8 x 8 = 64 (multiply the first digit by 8),
   64 + 1 = 65 (add the carry):
   the next digit is 5: _ _ 5 6. (Keep carry, 6.)
3. Square the first digit and add the carry, 6: 7 0 5 6.
4. So 84 x 84 = 7056.