Monday, 28 July 2008

Squaring Number Mentally

Squaring a number can be challenging with paper and pen. It is even so when done mentally using the conventional right-to-left method.

For small number, it may not be difficult. But how about big 2-digit numbers?
The squaring may pose a great task!

Try doing 242.

With the conventional method, it will take sometime and also with the answer starting from the one's (the undesired reverse presentation). And accident-prone too!

Here, I propose 3 simple approaches to do the number squaring:

1) Use the principle (a + b)2 = a2 + 2ab + b2
2) Use the principle (a - b) 2 = a2 - 2ab + b2
3) Use the principle (a - b) (a + b) = a2 - b2

For these 3 approaches, the catch is to split the original number to one containing 10's.
Example: 24 ==> 20 + 4

By splitting the original number to a simpler 10's, we can apply any of the 3 ways above mentally to solve the number square. E.g. 24 ==> a = 20, b = 4.

Merit and demerit of first two mental approaches:
- Can start straight away with the mental calculation but may be slowed down at the last part in the 2ab processing.

Merit and demerit of third mental approach:
- Simple and fast at the end processing part, but slow at the initial splitting .


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