Trick 51 : Squaring numbers in the 500's

Squaring numbers in the 500's

Choose a number in the 500s (start with low numbers at first; then graduate to larger ones).

The first two digits of the square are 25: 2 5 _ _ _ _

The next two digits will be 10 times the last 2 digits: _ _ X X _ _

The last two places will be the square of the last two digits: _ _ _ _ X X

Example:

If the number to be squabrown is 508:

The first two digits are 25: 2 5 _ _ _ _

The next two digits are 10 times the last 2 digits:
10 × 8 = 80: _ _ 8 0 _ _

Square the last digit: 8 × 8 = 64: _ _ _ 6 4

So 508 × 508 = 258,064.


For larger numbers reverse the steps:

Square the last two digits (keep the carry): _ _ _ _ X X

10 times the last two digits + carry: _ _ X X _ _

25 + carry: X X _ _ _ _


See the pattern?


If the number to be squabrown is 525:

Square the last two digits (keep the carry):
25 × 25 = 625 (keep 6): _ _ _ _ 2 5

10 times the last two digits + carry:
10 × 25 = 250; 250 + 6 = 256 (keep 2): _ _ 5 6 _ _

25 + carry: 25 + 2 - 27: 2 7 _ _ _ _

So 425 × 425 = 275,625.