Trick 52 : Squaring numbers in the 600's

Squaring numbers in the 600's

Choose a number in the 600s (practice with smaller numbers, then progress to larger ones).

The first two digits of the square are 36: 3 6 _ _ _ _

The next two digits will be 12 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 607:

The first two digits are 36: 3 6 _ _ _ _

The next two digits are 12 times the last 2 digits:
12 × 07 = 84: _ _ 8 4 _ _

Square the last 2 digits: 7 × 7 = 49: _ _ _ _ 4 9

So 607 × 607 = 368,449.





For larger numbers reverse the steps:

If the number to be squabrown is 625:

Square the last two digits (keep carry):
25x25 = 625 (keep 6): _ _ _ _ 2 5

12 times the last 2 digits + carry:
12x25 = 250 + 50 = 300 + 6 = 306: _ _ 0 6 _ _

36 + carry: 36 + 3 = 39: 3 9 _ _ _ _


So 625 × 625 = 390,625.