Squaring numbers in the 60s

1. Square the last digit (keep the carry)   _ _ _ X
2. Multiply the last digit by 12, add the carry   _ _ X _
3. The first digits will be 36 plus the carry:   X X _ _

   Example:

     If the number to be squared is 63:

1. Square the last digit (keep the carry):
       3 x 3 = 9 (keep 3)     _ _ _ 9
2. Multiply the last digit by 12, add the carry:
       12 x 3 = 36 (keep 3)    _ _ 6 _
3. The first digits will be 36 plus the carry:
       36 (+ carry): 36 + 3 = 39    3 9 _ _
4. So 63 x 63 = 3969.

   See the pattern?

     If the number to be squared is 67:

1. Square the last digit (keep the carry):
       7 x 7 = 49 (keep 4)     _ _ _ 9
2. Multiply the last digit by 12, add the carry:
       12 x 7 = 84, 84 + 4 = 88    _ _ 8 _
3. The first digits will be 36 plus the carry:
       36 (+ carry): 36 + 8 = 44  4 4 _ _
4. So 67 x 67 = 4489.

Use this pattern and you will be squaring these numbers with ease.