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 squared 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 squared 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.
|