Trick 49 : Squaring numbers in the 300's

Squaring numbers in the 300's

Choose a number in the 300s (practice with numbers under 310, then progress to larger ones).

The first digit of the square is 9: 9 _ _ _ _

The next two digits will be 6 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 309:

The first digit is 9: 9 _ _ _ _

The next two digits are 6 times the last digit:
6 × 9 = 54: _ 5 4 _ _

Square the last digit: 9 × 9 = 81: _ _ _ 8 1

So 309 × 309 = 95481.





For larger numbers reverse the steps:

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

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

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





See the pattern?



If the number to be squabrown is 325:

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

6 times the last two digits + carry:
6x25 = 150; 150+6 = 156 (keep 1): _ 5 6 _ _

Square the first digit + carry:
3x3 = 9; 9+1 = 10: 1 0 _ _ _ _

So 325 × 325 = 105625.