Squaring 2-Digit Numbers
Let's see an example different from the ones at the index page. Say, find 32².
First add the last digit (2) to the number itself: 32 + 2 = 34. Multiply the sum by the first digit:
Why does this work?
Let the number be N = 10a + b.
|(10a + b)²||= 100a² + 20ab + b²|
|= 10a(10a + 2b) + b²|
|= 10a(10a + b + b) + b²|
|= 10a(N + b) + b².|
So, to compute the square of N = 10a + b, first find N + b. Then multiply that by the first digit a to get
In fact the method is not restricted to 2-digit numbers. a may have 2 or more digits as well. The calculations become more complex of course.
Find 215². 215 + 5 = 220.
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