Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Oct 2014, 18:07

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

An easy way to find squares of numbers !!

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Intern
Intern
User avatar
Joined: 04 May 2012
Posts: 49
Location: Bangladesh
Concentration: Finance, Accounting
GMAT 1: 660 Q48 V32
GPA: 3.86
WE: Analyst (Venture Capital)
Followers: 2

Kudos [?]: 13 [3] , given: 59

An easy way to find squares of numbers !! [#permalink] New post 16 Sep 2013, 11:33
3
This post received
KUDOS
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. :)
Attachments

Finding Squares easily.pdf [65.51 KiB]
Downloaded 36 times

To download please login or register as a user

Manager
Manager
User avatar
Status: Dream big, work hard, and drink gallons of beer!
Joined: 11 Jun 2011
Posts: 213
Concentration: Finance, General Management
GMAT Date: 10-01-2011
WE: Web Development (Consulting)
Followers: 2

Kudos [?]: 13 [0], given: 33

Re: An easy way to find squares of numbers !! [#permalink] New post 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.
_________________

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!

Intern
Intern
User avatar
Joined: 04 May 2012
Posts: 49
Location: Bangladesh
Concentration: Finance, Accounting
GMAT 1: 660 Q48 V32
GPA: 3.86
WE: Analyst (Venture Capital)
Followers: 2

Kudos [?]: 13 [0], given: 59

Re: An easy way to find squares of numbers !! [#permalink] New post 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 ?? :)
2 KUDOS received
Manager
Manager
User avatar
Status: Dream big, work hard, and drink gallons of beer!
Joined: 11 Jun 2011
Posts: 213
Concentration: Finance, General Management
GMAT Date: 10-01-2011
WE: Web Development (Consulting)
Followers: 2

Kudos [?]: 13 [2] , given: 33

Re: An easy way to find squares of numbers !! [#permalink] New post 19 Sep 2013, 02:44
2
This post received
KUDOS
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!

Intern
Intern
User avatar
Joined: 04 May 2012
Posts: 49
Location: Bangladesh
Concentration: Finance, Accounting
GMAT 1: 660 Q48 V32
GPA: 3.86
WE: Analyst (Venture Capital)
Followers: 2

Kudos [?]: 13 [0], given: 59

Re: An easy way to find squares of numbers !! [#permalink] New post 19 Sep 2013, 02:47
great !! thanks.. got it :D
2 KUDOS received
Intern
Intern
avatar
Joined: 11 Jan 2012
Posts: 9
Location: India
Concentration: Operations, Finance
GMAT Date: 08-31-2012
GPA: 3.7
Followers: 0

Kudos [?]: 9 [2] , given: 11

GMAT ToolKit User
Re: An easy way to find squares of numbers !! [#permalink] New post 11 Oct 2013, 20:52
2
This post received
KUDOS
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 :)
Intern
Intern
User avatar
Joined: 04 May 2012
Posts: 49
Location: Bangladesh
Concentration: Finance, Accounting
GMAT 1: 660 Q48 V32
GPA: 3.86
WE: Analyst (Venture Capital)
Followers: 2

Kudos [?]: 13 [0], given: 59

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

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 :)


Superb buddy !! Thanks :D

+1 for the method !! :D
Re: An easy way to find squares of numbers !!   [#permalink] 11 Oct 2013, 21:37
    Similar topics Author Replies Last post
Similar
Topics:
Easily find the square of any number rknagoju 1 17 Jul 2012, 06:10
Root/ Exponents...easy way? Impenetrable 2 29 Dec 2011, 21:31
Ways to find the sum of consecutive odd/even numbers omomo 3 03 Nov 2005, 22:05
A woman has 11 close friends. Find the number of ways she MA 9 28 Apr 2005, 17:27
Find the numbers of ways in which 4 boys and 4 girls can be anirban16 9 19 Apr 2005, 17:23
Display posts from previous: Sort by

An easy way to find squares of numbers !!

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.