Squaring a 2-digit number ending in 7

1. Choose a 2-digit number ending in 7.
2. The last digit of the answer is always 9: _ _ _ 9
3. Multiply the first digit by 4 and add 4
   (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 47:
2. The last digit of the answer is 9: _ _ _ 9
3. Multiply the first digit (4) by 4 and add 4
   (keep the carry): 4 × 4 = 16, 16 + 4 = 20; the next
   digit of the answer is 0 (keep carry 2): _ _ 0 9
4. Multiply the first digit (4) by the next number (5)
   and add the carry (2):
   4 × 5 = 20, 20 + 2 = 22 (the first two digits): 2 2 _ _
5. So 47 × 47 = 2209.

See the pattern?

1. For 67 × 67
2. The last digit of the answer is 9: _ _ _ 9
3. Multiply the first digit (6) by 4 and add 4 (keep the
   carry): 4 × 6 = 24, 24 + 4 = 28; the next digit of the
   answer is 0 (keep carry 2): _ _ 8 9
4. Multiply the first digit (6) by the next number (7)
   and add the carry (2):
   6 × 7 = 42, 42 + 2 = 44 (the first two digits): 4 4 _ _
5. So 67 × 67 = 4489.
   

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