 Squaring Numbers in a Simple and Fun way

Squaring numbers is a tedious job if you do not know vedic maths shortcuts and other tricks and tips. Imagine having to waste your precious seconds in carrying out actual multiplications to find out squares during an exam. It can prove disastrous.

It is always advisable to learn various time saving tricks and alternate methods to find out percentages, fractions, squares, cubes, etc. because these will be useful in Quantitative Aptitude as well as Logical Reasoning sections of any competitive examination you take.

The idea of this post is contributed by Piyush Goel and it’s further edited by me to share with you a trend that he observed in squares of numbers.

If we talk about Square, Square is the result of multiplying a number by itself. So, square of 3 is 3×3=9. Similarly, square of 10 is 10×10=100. Since you know what is a square, observe this:

If we have to square 11, instead of 11×11=121,
we can simply put 1 (1*2)(1^2) and get 121.
Similarly, we can write the square of 12 as: 1(2*2)(2^2) and get 144. In the same fashion we can get the square of 13 as 1(3*2)(3^2)=169 and the square of 14 as 1(4*2)(4^2)=1|8|16 =196(after carrying over the 1 of 16 and adding it to 8).

Look at (2,4,6,8,10,12,14,16,18,20….difference of 2) & (1,4,9,16,25,36,49,64,81…….. difference is 3,5,7,9,11,13,15,17,19….) and difference of 3,5,7,9,11 is 2 so there is True Symmetry of 2.

11^2 = 1 2 1
12^2 = 1 4 4
13^2 = 1 6 9
14^2 = 1 8 16 = 100 + 80 + 16 = 196
15^2 = 110 25 = 100 + 100 + 25 =225
16^2 = 112 36 = 100 + 120 + 36= 256
17^2 = 114 49 = 100 + 140 + 49= 289
18^2 = 116 64 = 100 + 160 + 64= 324
19^2 = 118 81 = 100 + 180 + 81= 361
20^2 = 111^2 = 1 20 100 = 100 + 200 + 100 = 400
21^2 = 111^2 = 1 22 121 = 100 + 220 +121 = 441
22^2 = 112^2 = 1 24 144 = 100 + 240 +240 = 484
23^2 = 113^2 = 1 26 169 = 100 + 260+169 = 529
24^2 = 114^2 = 1 28 196 = 100 + 280+196 =576
25^2 = 115^2 = 1 30 225 = 100 +300 +225 =625
26^2 = 116^2 = 132 256 = 100 + 320 +256 =676
27^2 = 117^2 = 134 289 = 100 + 340 + 289 =729
28^2 = 118^2 =136 324 = 100 + 360 + 324 = 784
29^2 = 119^2 = 138 361 = 100 + 380 + 361 = 841
30^2 = 120^2 = 1 40 400 = 100 + 400 +400 =900
31^2 = 121^2= 121^2 = 1 42(111^2) =1 42 (1 22 121) =100 + 420 + 441 =961
41^2 = 131^2 = 1 62 (1 21^2) = 1 62 (1 42) (1 11^2) = 1 62 (1 42) (1 22 121) = 1 62 (961) = 100 + 620 + 961 = 1681

This is time saving and the best part is we do not have to mug up additional formulae or large algorithms of processes.

Piyush Goel, born on 10th February, 1967. He has a Diploma in Mechanical Engineering and a Diploma in Vastu Shastra. Always wanting to do something new, Mr. Goel has written 15 Spiritual and World Famous Books with his own hands in Mirror Image in different ways. He is now known as “Mirror Image Man”. He also has World’s First Hand-written Needle Book “Madhushala” to his credit.

Edited by Preeti Patawari Preeti Patawari

I'm here to share my love for numbers specially where I can help you clear your aptitude examinations like CAT, GMAT, IBPS and so on. In past I did that full time at Career Launcher.

7 thoughts to “Squaring Numbers in a Simple and Fun way”

1. Himesh says:

Yes as you mentioned I think it is absolutely right but I would like to say you do not discourage anybody work, everybody knows but some work can help some others who is doing RESEARCH on it and here want to clear have you read the article at the last the author wants to say There is “Symmetry of 2”.

2. Tom says:

There is always some formula behind any technique, which in this case is (a+b)^2=a^2 + 2ab + b^2. And the way you break down your a and b does make things increasingly harder as well, because computations would then rely on some previous squares of two-digits:

41^2 = 131^2 = 1 62 (1 21^2) = 1 62 (1 42) (1 11^2) = 1 62 (1 42) (1 22 121) = 1 62 (961) = 100 + 620 + 961 = 1681

However, if you see 41^2 as (40+1)^2, then you just get 1600 + 80 + 1 = 1681. This also puts less strain on our short-term memory too.

1. mitali says:

sir you right but when we study deep we brings new things into existence which boost ours knowledge.There are more methods.

Well done Mirror Image Man Piyush

2. Vineet Patawari says:

Hey Tom,

You’re bang on. Every trick is derived from some underlying formula already known to most of us. Even those algebric formulas we’ve learned in schools and colleges are ways of making simpler by breaking them in simpler steps.

Thanks
Vineet

3. MURALI says:

It’s easy method. but if u would have explained for some more numbers that may clear the method to students like 31, 51 etc.,

1. P S Shami says:

There are several simple and smart ways of squaring numbers. I would advise you to memorize squares table up to 25. Probably you know square table up to 15. squares of 20 and 25 are known to every body. examine squares up to 100 , you will find last two digits of squares will be same for only 4 numbers between 1 to 100. For example 44. It is last two dihits of square of 12. now 44 will be last two digits for number 12 below and 12 above 50 i.e 38 and 62. It will be last digits in squres of number 12 below 100 which is 88. check for all numbers from 1 to 25.

squares from 51 to 59 are simplest and you can do in just 3 seconds. See the answer will be of 4 digits. first two digit will be 5X5+ digit at unit place. last two digits will be square of digit at unit place. Exp square of 58 will be |25+8|64=3364. Square of 53 =25+3|09=2809, square of 51= 25+1|01=2601 etc.. Observe first two digits of squares from 41 to 59 are 20,21,22,23,…..33,34. look for what are last two digit numbers. You may easily remember all squares from 41 to 59. There are a number of simple ways to calculate squares mentally.

1. himesh says: