Squaring numbers in the 40s

1. Square the last digit (keep the carry)   _ _ X
2. Multiply the last digit by 8, add the carry   _ X _
3. The first digits will be 16 plus the carry:  X X _ _

   Example:

     If the number to be squared is 42:

1. Square the last digit:
       2 x 2 = 4    _ _ _ 4
2. Multiply the last digit by 8:
       8 x 2 = 16    _ _ 6 _
3. The first digits will be 16 plus the carry:
       16 (+ carry): 16 + 1 = 17  1 7 _ _
4. So 42 x 42 = 1764.

   See the pattern?

     If the number to be squared is 48:

1. Square the last digit (keep the carry):
       8 x 8 = 64 (keep 6)    _ _ _ 4
2. Multiply the last digit by 8, add the carry:
       8 x 8 = 64, 64 + 6 = 70 (keep 7)  _ _ 0 _
3. The first digits will be 16 plus the carry:
       16 (+ carry): 16 + 7 = 23  2 3 _ _
4. So 48 x 48 = 2304.

With some practice you will be giving these squares quickly.