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Tuesday, 1 September 2015

Quantitative Aptitude shortcuts for IBPS, RBI, SBI PO : Find square of a number

If you really want to stand out in a competitive examination you need to be different from others. 'Different' in the sense that you must be able to attempt more number of questions than the others, in other word, you must be a efficient solver. For that to happen, you need to go faster than the others and attempt maximum number of problems in that given duration of time. With traditional methods of solving problems, you can't go faster. The traditional ways that we had learned in schools was well enough to pass out a school exam, but for cracking a IBPS, SBI PO, RBI or SSC exams, that's not really going to help much. For that you need to go for shortcuts. The more you learn the shortcuts, the more number of questions you will be able to attempt. This is our first post on Shortcut techniques series. In this article you will learn the shortcuts to find out the square of a number. Before going to the methods, let me tell you simply knowing the shortcuts wouldn't likely to work on examination. Only continuous practice could make you efficient. So practice the methods as much as you can. 

There are several techniques to find out square of a number. Some methods are confusing, that means, have different variations like from 10 to 50, you need to follow a different technique, again 50-80, 80-100, all have little variations in the methods that could make you confuse-which was the particular method for a particular range of numbers. So omitting such types of methods, we have come up with some really simple techniques which you can easily remember and by applying them you will be able to find out square of a number in a few seconds. Let's check out the methods- 


Find_square_tricks, Maths_tricks


First Method 


You can try this method for finding out square of any two digit numbers. First add or subtract a number from the given number such that one of the operation (addition or subtraction) generates a number which is nearest multiple of ten. Multiply both the results of addition and subtraction and add the added or subtracted number to it. Things will be clear when take a look on the examples- 
Suppose we need to find square of 42. 

42² = (42-2) x (42+2) + 2² 
      = 40 x 44 + 4 
      = 1760 + 4 = 1764 

36² = (36-4) x (36+4) + 4² 
      = 32 x 40 + 16 
      = 1280 + 16 = 1296 

55² = (55+5) x (55-5) + 5² 
      = 60 x 50 + 25 
      = 3000 + 25 + 3025 

Second Method 


By using this method you can find square of any two digit as well as three digit numbers. First add the two digit and take square over it so that it becomes in the format of  (a + b)². Now write it as per formula (a + b)² = a² + 2ab + b². Then take the one-th position digit of the b² term, other digits will go to the term 2ab as carry, then again taking the one-th position digit, other digits on the left will be added to a² term as carry. Let's clear it in straight- 

42² = (4+2)² 
      = 4² + 2x4x2 + 2² 
      = 16  +  16  +  4 
                           
          17       6       4 
               Carry1 Carry0 
      = 1764 

76² = (7+6)² 
      = 7² + 2x7x6 + 6² 
      = 49 + 84 + 36 

Now 36 = 6 → carry 3 
         84 = 84 + carry 3 = 87 = → carry 8 
         49 = 49 + carry 8 = 57 

Therefore, answer is 5776. 

Similarly, 124 ² can be done by solving (12+4)². Try it yourself. 

Third Method 


This method is for the numbers having 5 in one-th position. Last two digit will be 25 as 5x5 = 25. 
The other digit is multiplied to its next digit. Combining both the results the square is obtained. 

Suppose for 45² 

4x(4+1) = 4x5 = 20 

5 x 5 = 25 

Hence 45² = 2025 

Hope you have understood the tricks. If you have any doubts you can ask in the comment section. Also you can share your tricks with our readers. 

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