Trick 62 : Squaring numbers between 7000 and 7099

Squaring numbers between 7000 and 7099

Choose a number between 7000 and 7099.

The first three digits are: 4 9 0 _ _ _ _ _

The next two digits are 4 times the last two digits,
with zero added: _ _ _ 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 7004:

The first three digits are: 4 9 0 _ _ _ _ _

The next two digits are 4 times the last two, with zero added:
4 × 4 = 16; 16 + 40 = 56: _ _ _ 5 6 _ _ _

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

So 7004 × 7004 = 49,056,016.



See the pattern?



For numbers greater than 7007, reverse the order:

If the number to be squabrown is 7025:

For the last three digits, square the last two:
25 × 25 = 625: _ _ _ _ 6 2 5

For the middle two digits, add zero to the last two,
then add 4 times the last two:
250 + 4 × 25: 250 + 100 = 350 (keep carry):
_ _ _ 5 0 _ _ _

The first three digits are 490 + the carry:
490 + 3 = 493: 4 9 3 _ _ _ _ _

So 7025 × 7025 = 49,350,625.