An easy way to find squares of numbers !!

Question

Hello. I have just discovered an interesting way to find out squares of numbers. Well, its not anything magical, but its interesting and can be helpful sometimes if you can do fast addition and subtraction. In this method, if you know the square of 20, u can find the square of 19 & 21 by simple subtraction & addition. Yap. It works this way. If you dont know the square of any number, its not gonna work

!! so, lets see an example: 20^2 = 400 ( we all know ). But what is 19^2 ? or what is 21^2 ?? finding out the square of both this numbers looks challenging to me, if I use multiplication. so, heres the trick: to find out 19^2, subtract (20+19)=39 from 400. u get 361. This is the square of 19. Similarly, to find the square of 21, add (20+21) = 41 to 400. its 441 and it is the square of 21. Similarly, if we know 30^2 = 900. We can easily find out, 29^2 = 900 - (30+29) = 841. and 31^2 = 900 + (30+31) = 961.. even we can stretch it to 28 and 32 as now we know the square of 29 & 31 I know its nothing super magical, but i felt very happy to figure out this relationship, which, I believe, will be very helpful sometimes.. For those of you who are interested to know how it works ( some of you might have even found it out already ): Its simple algebra. If we know the square of the number x, we can find the square of number (x+1) and (x-1). (x+1)^2 = x^2 + 2x + 1 = x^2 + ((x) + (x+1)) -- thats what we did for 21^2 when we assumed we know 20^2 (x-1)^2 = x^2 - 2x + 1 = x^2 - ((x) + (x-1)) -- thats what we did for 19^2 when we assumed we know 20^2 Hope it will help you sometimes.. Consider Kudos if you find it helpful. I have attached a pdf version of this post so that you can save it for later reference incase u need.

sguptashared · Answer

This is awesome!

I also found something recently, in questions were you are given sum of 2 numbers and have to find the greatest number when you multiple 2 numbers such as x+y = 16. The greatest number would be a square i.e., 8*8 in this case.

Please give a kudos if you found this useful.

AsifBD · Answer

thanks sguptashared !! However, I didn't get your technique clearly

Will you please elaborate a little bit more and also add a question as example ??

sguptashared · Answer

For example- What are the values of x and y at which we have the maximum value, when x+y=16

The maximum value would be when both x and y are equal to 8.

For instance, if we take x=7 y=9, we get 63
and if we take x=1 y=15 we get 15. The closer the 2 numbers, the higher their values.

Please give a kudos if you found this useful.

AsifBD · Answer

great !! thanks.. got it :D

sagiyer · Answer

Hi all, Here is another method to find squares of ANY 2 digit number in a matter of seconds

For that you would need to remember squares of numbers upto 25, which I believe most of us know. So, here goes: say 44^2. check difference with the number 25 - In this case, 44-25 = 19 Then check difference with 50 - In this case, 50-44=6. square this difference, i.e - 6^2 = 36 Now, join the 2 numbers...1936..there you go, that's your answer

A slightly more difficult number this time - Say 71 Step 1 ... 71-25 = 46 Step 2 ... 71 - 50 = 21...21 squared = 441...since we have to ensure we stick to 2 digits only, carryover the hundreds digit (4), by adding it to 46..so the result from step 1, now becomes 46+4 = 50 So, your answer is 5041

AsifBD · Answer

Superb buddy !! Thanks

+1 for the method !!

An easy way to find squares of numbers !!

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards