Trick 50 : Squaring numbers in the 400's

Squaring numbers in the 400's

Choose a number in the 400s (keep the numbers low at first; then progress to larger ones).

The first two digits of the square are 16: 1 6 _ _ _ _

The next two digits will be 8 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 407:

The first two digits are 16: 1 6 _ _ _ _

The next two digits are 8 times the last 2 digits:
8 × 7 = 56: _ _ 5 6 _ _

Square the last digit: 7 × 7 = 49: _ _ _ 4 9

So 407 × 407 = 165,649.


For larger numbers reverse the steps:

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

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

16 + carry: X X _ _ _ _


See the pattern?



If the number to be squabrown is 425:

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

8 times the last two digits + carry:
8 × 25 = 200; 200 + 6 = 206 (keep 2): _ _ 0 6 _ _

16 + carry: 16 + 2 = 18: 1 8 _ _ _ _

So 425 × 425 = 180,625.