Trick 48 : Squaring numbers in the 200's

Squaring numbers in the 200's

Choose a number in the 200s (practice with numbers under 210, then progress to larger ones).

The first digit of the square is 4: 4 _ _ _ _

The next two digits will be 4 times the last 2 digits: _ X X _ _

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

Example:
If the number to be squabrown is 206:

The first digit is 4: 4 _ _ _ _

The next two digits are 4 times the last digit:
4 × 6 = 24: _ 2 4 _ _

Square the last digit: 6 × 6 = 36: _ _ _ 3 6

So 206 × 206 = 42436.





For larger numbers work right to left:

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

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

Square the first digit + carry: X _ _ _ _





See the pattern?



If the number to be squabrown is 225:

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

4 times the last two digits + carry:
4x25 = 100; 100+6 = 106 (keep 1): _ 0 6 _ _

Square the first digit + carry:
2x2 = 4; 4+1 = 5: 5 _ _ _ _

So 225 × 225 = 50625.