Quicker Maths

Squaring any 2-digit number

Posted on December 7, 2010

A guest post by Maria Rainier

Shortcut to Squaring Any 2-Digit Number

What do you do when your calculator has been confiscated and the world is depending on you to square a two-digit number within a minute? Don’t panic – just follow three simple steps that require basic addition and multiplication, and you’ll be able to solve the problem in no time. If you practice enough, you’ll even be able to complete each step mentally, rendering scratch paper unnecessary. This will save you time on drills and strengthen your skills so you can tackle other challenges. Eventually, you’ll be able to solve multi-step squaring problems without ever breaking a sweat – or a pencil.

This is a trick I learned during my old MATHCOUNTS days, but it comes in handy for lots of other competitive math as well. It was great for sprint, team, target, and countdown problems, but now it just comes as second nature whenever I run into a more complex problem that involves a squaring step. If you’re having trouble squaring two-digit numbers on the fly without a calculator, give this method a try. It seems a bit cumbersome at first, but as you practice, you’ll be able to speed up the process and get your answer within seconds.

3 Steps for 2-Digit Squares

Let’s work through the steps with an example to better demonstrate the process. Imagine that you’re expected to square 83 quickly and accurately – the following steps will help you complete the task.

1. Square each digit individually, making sure that you get a two-digit number for each square. If the number is low and its square gives you only one digit, use 0 as a placeholder.

8² = 64 and 3² = 9 = 09, giving you 6409

2. Now, multiply the two digits and double your answer, adding a 0 to the end.

8 X 3 = 24; 24 X 2 = 48, giving you 480

3. Simply add your answers from steps one and two.

6409 + 480 = 6889, or 83²

Isn't this very simple? Do you know any other such method for squaring?

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Posted by Vineet Patawari

1. I kept encountering so many tricks..but the problem with those tricks was umpteen divisions: 20-30, 50-60,etc.
However this method of yours is amazing and it’s uneqivocalness impressed me a lot.I will keep following your site to enlighten myself with such amazing tricks.
Kudos

2. nice trick, well done

3. niceeeeeeeee

4. Ohh man i thought i discovered it!!!
a few months ago and now i stumble upon this site and all my dreams shatter!
71^2
1
7
7
49
631
this was my method. but the method above is the same.

5. superb tricks,thanx

6. very nice

7. For 13^2
We can also use (a+b)^2 & result is same.

8. thanks…………..

9. hello Friends,
i want to know formulas of 25^48 like this plzzzz

10. very nice. Vineet you Rock.

11. AWESOME

12. its a terrific trick fr squring

13. Thank u So much…

14. Its great trick for all .Thanks

15. awsum

16. i liked it….
Its a great trick..

17. Its awesome.

• Thanks Hyder! Appreciate the kind words.

18. But how does all this vedic math work?Doesn’t it have any logic behind it.Just things happen like that.I dont think think so.The real challenge lies in finding out what that logic is.

• Dear Pavan,

Everything in vedic maths have got a logic. For example the logic behind the above trick is very simple – it’s writing the 2 digit no. in (a+b)^2 format which is equal to a^2 + b^2 + 2ab. Hope you get it now.

19. hey there is a correction for the method i have mentioned
it works for any no. Other than 1digit no. When doing operation on three digits take left two digit as tens and the right one as one

• Dear Yash,

You are correct. It will work for any number, but as you increase the no. of digits the calculations will become little difficult. Nevertheless, with practice you can master the trick.

20. hey there is another method
for 83*83
first add the ones digit to the no. And multiply it by tens digit
8*(83+3)
square the ones digit
3*3 gives 09
we got 8*86 , 09
688 , 09
add tens of right no. To the left no.
Gives 6889
this technique works for any no.

• how it works for 3 digit no..
and four digit no..

• abi says the true..
same problem..
need the explanation for three and four digit..

• It may not be very effective for 3 digits but still I’ll give you the process –

say u want to find 321^2

step 1. 3^2 = 9 and 21^2 = 0441; combining the numbers we get 90441
step 2. (2*3*21)*100 = 12600

Adding 90441 + 12600 = 103041

21. for squaring 2 digit number ending wid 5 there’s another trick
consider 65^2
now the number in the tenth digit+1 is multiplied by itself adding 25 at the end
for instance 6(here in 10th digit) is multiplied wid 6+1 i.e 6*(6+1) + 6*7 = 42
now add 25 at the end tht will give you 4225 = 65^2

22. nice
indian vedic maths baap-cheez hai…

23. shilpa its fine

24. Wow it was a great trick

25. this is simply great

26. this gives wrong answer for 12 and 13 no

• 12^2 = 144

via the given algorithm: 1^1=1 , 2^2=4 => 0104 = 104
1*2=2 => 2*2=4 => 40
104+40=144

Hence, it works for 12.

Also works for 13. Pf left to reader.

• 13^2 = 169

1^1=1 , 3^2=9 => 0109 = 109
1*3=3 => 3*2=6 => 60
109+60=169

• actually u don’t understand the method that’s it does not work for you and don’t misguide any one because it helps lot

27. this is an identity used ie (a+b)2=a2+b2+2ab
here (83)2= (80)2+(3)+2(80)(3)

• (80+3)=(80)2+(3)2+2*80*3
= 6400+9+480
= 6889

• nice noticing man..
gud job…