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Tricks to Calculate Square of a Number quickly

Updated on September 8, 2014

Maths is a very interesting subject. It waves the human knowledge through thinking and calculative powers. Maths is not just for learning but used in day today life, like purchasing something, counting something, exchange of money etc.

There are many problem in maths which we can solve with traditional methods, while it is good way of doing and learning but not for competitive exams. Hence to get better score than others in competitive exams we need to know some useful tricks, which save time as well as boost the score. In Bank PO, if you know some good tips and tricks - shortcuts for quantitative aptitude you will surely score higher than other.

To help you and other bank aspirants in this hub we are going to learn some tricks for calculating squares. We are going to learn how to calculate square of any number quickly. Follow the instructions and steps given below and boost your score in bank exam or other exam where quantitative aptitude will helps you gain score.

Table of Contents

  1. Square of numbers from 1 to 30
  2. Square of Numbers ending with 5
  3. Square of Numbers between 51 to 59
  4. Get square of Numbers with base 10,100,1000....
  5. General Formula to find square of any Number

Square of Number 1-30

Number
Square
Number
Square
Number
Square
1
1
11
121
21
441
2
4
12
144
22
484
3
9
13
169
23
529
4
16
14
196
24
576
5
25
15
225
25
625
6
36
16
256
26
676
7
49
17
289
27
729
8
64
18
324
28
784
9
81
19
361
29
841
10
100
20
400
30
900

Find Squares of Numbers ending with 5

One of the easiest things we learn to calculate square of a number which ends in 5. It is very easy to remember and answer comes in no time.

To find square of any number that ends with 5 follow the steps -

  1. Break the number in two parts - only 5 and rest of the numbers.
  2. Add one to the rest of numbers (Find successor of the number).
  3. Multiply the number separated with 5 to it successor.
  4. Get the square by just putting the number obtain in step 3 and '25' in right of it.

Example 1 : Find square of 45?

We have two part - '4' and '5'. Successor of 4 is 5. Product of the two numbers (4 and it successor, by step 3) we get - 4 X 5 = 20. Hence ans were is 2025 (by step4).

So Square of 45 is 2025.

Example 2 : Find square of 125?

We have - 12 and 5 as two parts. Successor of 12 is 13 and their product is 156. So square of 125 would be 15625.

You can do it in no second just multiply the number before 5 with it successor and put 25 to obtain the squares.

Square of Number with base 10 ,100,1000...

For base 10 square of number is easy to find, as you may remember from the table given above. If you forgot follow the rules which will be given here

We Start with the number having base 100. Let Do this with examples.

  • Example 1 : Square of 103?

We are going to find square of number 103 which is a 3 digit number or with base 100. Hence for square we put three places.

Since 103 is 3 more than 100(the base) we add 3 to the number itself. Here we got 103+3=106; This number will be placed to leftmost place (see the figure).

Next Find the square of 3 (as number is 3 more than base) which is 9. We place this to rest of the remaining places we decided. Since 9 is single digit but we have two places left, so add zero before 9 to make it 09.

Now we have 106 is for leftmost part, 09 for remain two place. Hence Square of 103 is 10609.

  • Example 2 : Square of 97?

97 is 3 less than 100 so subtract 3 from 97. Here also we will place 3 place so put that 96 at leftmost place. Rest of the two places will be fill with the square of 3 i.e 9, but we put 09 to make two place get filled.

Hence the square of 97 will be 9409.

Find Square of number from 51 to 59 easily

It is very easy to find square of number lies between 50 and 60 that numbers from 51 to 59. You don't need to brush the square just find it at no time. If you remember the square of 100 number than you chances of calculating faster is very high. If you don't follow the trick for number from 51 to 59.
We know 51 to 59 number lies on the base of 25. We take them at base 25 to calculate the square in no time.

  1. Find by how much number is greater than 50, say 51 is 1 more than 50.
  2. Then add that number obtain in step 1 to 25. Say for 51 we get 1 so adding 1 to 25 gives 26.
  3. We will have 4 digit number as square so put square of number obtained in step 1 at unit and tenth places. For 51 we have 1 so square of 1 is 1 hence we will put 01. Next put number obtains in rest of the 2 places. Like for 51 we have 26. Hence obtain the answer. Incase of 51 we get 2601.

Example 1 : Square of 54?

54 - 50 =4, hence first two place will be square of 4 that is 16. Rest two place will be 25+4 = 29. Hence square the square of 54 is 2916.


General Formula to Find square of any Number Quickly

There is a simple general formula to find the square of any number at no time. The formula is given as below -

(ab)2 = a2.2ab.b2

* b is unit digit of the number, a is rest digits of the number. In right hand side - b is unit place, 2ab at tenth place and rest part is a.

Now Lets understand the formula. Here we have a number ab with b as unit digit and a the other part of the number. Remember this only and we can calculate the square easily.

Example 1 : Square of 23?

In 23 we have a=2 and b=3 so we have,

a2 = 4, 2ab = 12, b2 = 9

Hence number will be 4.12.9, since only one digit can be at tenth place so take the one to other hundredth place here, then add. So the square of 23 will be 529

Example 2 : Square of 112?

a=11, b=2 for this number

a2 = 121, 2ab = 44 and b2 = 4 so number we have 121.44.4, We add the 4 taking it to hundredth place. Hence number obtain is 12544 which is correct answer.

Point to remember - we have b2 at unit place and 2ab at tenth place for the square so if you get two digit, make sure take the leftmost (tenth part of that) to next place and add it up to obtain the correct squares.

Test your learning skills


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Summary of the Contents

We have learn many methods to calculate the squares. Let summarise it in easy and simple way.

Square of X5 is [(x+1)*x]25

Square of 5X, where X=1 to 9 is [25+X]X2 Where X2 is two digit number(add zero 01 for 1, 04 for 4 etc)

Square of 100+X is [100+X+X]X2 where X2 is a three digit number (add to to make them three digit like 001 for 1, 004 for 4)

Square of 100-X is [100-X-X]X2 where X2 is a three digit number

Similarly you can create for base 1000 etc. If you know any of the other great ways to find the square easily in no time please tell in comments. Don't hesitate to ask anything.

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    • profile image

      Rajesh 2 years ago

      Wonderful great ways to find squares in little time. Bank PO aspirants will definitely need to learn and practice these shortcut methods to brush up their calculation skills.

    • profile image

      Himesh 2 years ago

      Great tricks for squares thanks for sharing!

    • Bluelotusrajeev profile image
      Author

      Rajeev Kumar 2 years ago

      hi! Himesh

      Thanks for appreciation

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