Squaring Numbers in the 300s

Squaring numbers in the 300s

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 squared 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 squared 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.