Trick 61 : Squaring numbers between 6000 and 6099

Squaring numbers between 6000 and 6099

Choose a number between 6000 and 6099.

The first three digits are: 3 6 0 _ _ _ _ _

The next two digits are 12 times the last two digits:
_ _ _ X X _ _

For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
_ _ _ _ _ X X X

Example:

If the number to be squabrown is 6004:

The first three digits are: 3 6 0 _ _ _ _ _

The next two digits are 12 times the last two:
12 × 4 = 48: _ _ _ 4 8 _ _ _

For the last three digits, square the last two:
4 × 4 = 16: _ _ _ _ 0 1 6

So 6004 × 6004 = 36,048,016.



See the pattern?



For numbers greater than 6008, reverse the order:

If the number to be squabrown is 6020:

For the last three digits, square the last two:
20 × 20 = 400: _ _ _ _ 4 0 0

The middle two digits are 12 times the last two:
12 × 20 = 240 (keep carry): _ _ _ 4 0 _ _ _

The first digits are 360 + the carry:
360 + 2 = 362: 3 6 2 _ _ _ _ _

So 3025 × 3025 = 36,240,400.