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| Home » Maths Tricks » Squaring Numbers In The Five Hundreds |
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| Maths Tricks of Squaring Numbers In The Five Hundreds |
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Squaring numbers in the five hundreds |
Choose a number in the 500s (start with low numbers at first; then graduate to larger ones).
The first two digits of the square are 25: 2 5 _ _ _ _
The next two digits will be 10 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 508:
The first two digits are 25: 2 5 _ _ _ _
The next two digits are 10 times the last 2 digits:
10 x 8 = 80: _ _ 8 0 _ _
Square the last digit: 8 x 8 = 64: _ _ _ 6 4
So 508 x 508 = 258,064.
For larger numbers reverse the steps:
Square the last two digits (keep the carry): _ _ _ _ X X
10 times the last two digits + carry: _ _ X X _ _
25 + carry: X X _ _ _ _
See the pattern?
If the number to be squared is 525:
Square the last two digits (keep the carry):
25 x 25 = 625 (keep 6): _ _ _ _ 2 5
10 times the last two digits + carry:
10 x 25 = 250; 250 + 6 = 256 (keep 2): _ _ 5 6 _ _
25 + carry: 25 + 2 - 27: 2 7 _ _ _ _
So 425 x 425 = 275,625.
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