Squaring a 2-digit number ending in 9

1. Choose a 2-digit number ending in 9.
2. The last digit of the answer is always 1: _ _ _ 1
3. Multiply the first digit by 8 and add 8 (keep the carry): _ _ X _
4. Multiply the first digit by the next consecutive number and
   add the carry: the product is the first two
   digits: XX _ _.

   Example:

1. If the number is 39:
2. The last digit of the answer is 1: _ _ _ 1
3. Multiply the first digit (3) by 8 and add 8 (keep the
   carry): 8 x 3 = 24, 24 + 8 = 32; the next digit of
   the answer is 2 (keep carry 3): _ _ 2 1
4. Multiply the first digit (3) by the next number (4)
   and add the carry (3): 3 x 4 = 12, 12 + 3 = 15
   (the first two digits): 1 5 _ _
5. So 39 x 39 = 1521.

   See the pattern?

1. For 79 x 79
2. The last digit of the answer is 1: _ _ _ 1
3. Multiply the first digit (7) by 8 and add 8 (keep the
   carry): 8 x 7 = 56, 56 + 8 = 64; the next digit of
   the answer is 4 (keep carry 6): _ _ 4 1
4. Multiply the first digit (7) by the next number (8)
   and add the carry (6): 7 x 8 = 56, 56 + 6 = 62
   (the first two digits): 6 2 _ _
5. So 79 x 79 = 6241.

Practice other examples using this pattern, and in no time you'll be able to give these squares faster than someone using a calculator.