Trick 60 : Squaring numbers between 5000 and 5099

 Squaring numbers between 5000 and 5099

Choose a number between 5000 and 5099.

The first three digits are: 2 5 0 _ _ _ _ _

The next two digits are 10 times the last two digits:
2 5 0 X X _ _ _

For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
2 5 0 _ _ X X X

Example:

If the number to be squabrown is 5004:

The first three digits are: 2 5 0 _ _ _ _ _

The next two digits are 10 times the last two:
10 × 4 = 40: _ _ 4 0 _ _ _

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

So 5004 × 5004 = 25,040,016.



See the pattern?



For numbers greater than 5011, reverse the order:

If the number to be squabrown is 5012:

For the last three digits, square the last two:
12 × 12 = 144: _ _ _ _ 1 4 4

The middle two digits are 10 times the last two (keep the carry):
10 × 12 = 120 (keep carry of 1):
_ _ _ 2 0 _ _ _

The first three digits are 150 + the carry:
250 + 1 = 251: 2 5 1 _ _ _ _ _

So 5012 × 5012 = 25,120,144.