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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Getting the square of a number ending with 5 is very easy.

If the last digit of the number is 5, then the second part of the result will be 25 and for the first part of the result, multiply the number(leaving 5 i.e the last digit) with the next integer.

Ex: 35*35= 1225 { First part : 3*4=12 , Second part: 25 } 245*245=60025 { First part : 24*25=600 , Second part: 25 }

Ok now it is simple to calculate squares of a number ending with 5.

How to calculate square of any number??

26*26=???

The following is a Very important property of squares:

1*1= 1 = 1 2*2= 4 = 1+3 3*3= 9 = 1+3+5 4*4= 16 = 1+3+5+7 an so on...

i.e. Square of a number "n" is equal to sum of first "n "odd numbers.

"n" th odd number for the above sequence is given by 2n-1

26*26=???

For calculating this you must use the result 25*25(which we have already learned)

26*26=25*25+26th odd number = 625+2(26)-1 = 676

27*27= 25*25+ 26th odd no + 27th odd no but sum of 26th +27th odd numbers= 26(4) {similarly in other cases} = 625+26*4 = 729

Traditional multiplication would seem better for the above mentioned examples but this would really fetch you for 3digit numbers. When you apply this concept with 3 digit numbers you will understand the beauty of the above mentioned technique.

Re: Easily find the square of any number [#permalink]

Show Tags

17 Jul 2012, 18:07

Quite interesting (though I'm too lazy to verify it). I don't think it's faster than an old-fashioned multiplication but that can be useful to double check the result.

Thanks

gmatclubot

Re: Easily find the square of any number
[#permalink]
17 Jul 2012, 18:07

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...