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.

Please share your feedback and other interesting ways that you know.

About The Author :

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

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