An easy way to find squares of numbers !! : GMAT Quantitative Section
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# An easy way to find squares of numbers !!

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An easy way to find squares of numbers !! [#permalink]

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16 Sep 2013, 11:33
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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

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.
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Finding Squares easily.pdf [65.51 KiB]

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Re: An easy way to find squares of numbers !! [#permalink]

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18 Sep 2013, 12:05
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.
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If I look absent-minded or insane, I am just living a dream of being successful. If you still wonder why I am like this, you have no idea how success tastes like!

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Re: An easy way to find squares of numbers !! [#permalink]

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18 Sep 2013, 21:00
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 ??
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Re: An easy way to find squares of numbers !! [#permalink]

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19 Sep 2013, 02:44
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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.
_________________

If I look absent-minded or insane, I am just living a dream of being successful. If you still wonder why I am like this, you have no idea how success tastes like!

Current Student
Joined: 04 May 2012
Posts: 76
Concentration: Finance, Accounting
GMAT 1: 660 Q48 V32
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Kudos [?]: 20 [0], given: 66

Re: An easy way to find squares of numbers !! [#permalink]

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19 Sep 2013, 02:47
great !! thanks.. got it :D
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Re: An easy way to find squares of numbers !! [#permalink]

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11 Oct 2013, 20:52
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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

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

Current Student
Joined: 04 May 2012
Posts: 76
Concentration: Finance, Accounting
GMAT 1: 660 Q48 V32
GPA: 3.86
WE: Analyst (Venture Capital)
Followers: 8

Kudos [?]: 20 [0], given: 66

Re: An easy way to find squares of numbers !! [#permalink]

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11 Oct 2013, 21:37
sagiyer wrote:
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

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

Superb buddy !! Thanks :D

+1 for the method !! :D
Re: An easy way to find squares of numbers !!   [#permalink] 11 Oct 2013, 21:37
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