The earlier trick for finding the square was a more generic one and can be implemented to find out the square of any number. You can find the trick here:
http://conceptsforcat.blogspot.com/2009/03/trick-for-squares-of-number.html
However, at points it is time consuming and needs good multiplication skills.
This trick is a more specific one to find out the square of any number between 25 and 75.
The only pre-requisites for this trick is the knowledge of the squares of 1 to 25.
So it goes this way:
1. Assume the number to be X.
2. Let the difference of the number from 25 be Y i.e. Y = (X - 25)
3. Let the difference of the number from 50 be Z i.e. Z = (X - 50)
4. The square of the number will be [(100 x Y) + (Square of Z)].
The above trick can be explained from the following examples:
Eg1. Let the number be 33 i.e. X = 33
Hence, Y = (X - 25) = (33 - 25) = 8
Also, Z = (X - 50) = (33 -50) = - 17
Therefore the square of X = [(100Y) + (Square of Z)]
= [(100 x 8) + (-17 x -17)]
= 800 + 289
= 1089.
i.e. Square of 33 = 1089.
Eg2. Let the number be 53 i.e. X = 53
Hence, Y = (X - 25) = (53 - 25) = 28
Also, Z = (X - 50) = (53 -50) = 3
Therefore the square of X = [(100Y) + (Square of Z)]
= [(100 x 28) + (3 x 3)]
= 2800 + 9
= 2809.
i.e. Square of 53 = 2809.
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