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Funny. Yesterday I was telling my wife how I calculated 97 x 97 in my mind (For a problem she was trying to solve). I obviously used (a-b)^2. But when I told how it's done, my wife said .. she'd rather multiply 97s

Re: shortcut for squares? [#permalink]
18 May 2007, 21:45

bmwhype2 wrote:

Himalayan wrote:

bmwhype2 wrote:

is there a shortcut to quickly calculate a square of a number? let's say 28 squared...

= (30 - 2)^2 = 900 - 120 + 4= 784

nice. but its more tedious than multiplying 28x28.

what is the square of 57?

1. 3212
2. 3230
3. 3241
4. 3244
5. 3249

in this case you can easily pick 5 because 7 x 7 (unit digits) is 9. so we can take the clue like this. but if answer choices are all or some are with 9 as unit digits, then it is really time consuming and we should follow either formula or multiplication.....

Re: shortcut for squares? [#permalink]
19 May 2007, 05:09

Hi,
This can be done using Vedic mathematics( though not required for GMAT) nevertheless please see below.

Example : Suppose we have to multiple 12 by 13

1. We multiply the left hand most digit 1 of the multiplicand vertically by the left hand most digit 1 of the multiplier , get their product as 1 and set it down as the left-hand-most part of the answer;
2. We then multiply 1and 3, and 1 and 2 cross-wise , add the two, get 5 as the sum and set it down ad the middle part of the answer ; and
3. We multiply 2 and 3 vertically , get 6 as their product and put it down as the last right-hand-most part of the answer.

Thus 12 x 13 = 156

12
13
___________
1:3+2:6=156

Coming back to the problem at hand we need 28 x 28

Answer is (2*2+ carry forward from prev) : (2*8 +2*8+ carry forward from prev): ( 8x8)

Re: shortcut for squares? [#permalink]
19 May 2007, 08:56

manish.gmat wrote:

Hi, This can be done using Vedic mathematics( though not required for GMAT) nevertheless please see below.

Example : Suppose we have to multiple 12 by 13

1. We multiply the left hand most digit 1 of the multiplicand vertically by the left hand most digit 1 of the multiplier , get their product as 1 and set it down as the left-hand-most part of the answer; 2. We then multiply 1and 3, and 1 and 2 cross-wise , add the two, get 5 as the sum and set it down ad the middle part of the answer ; and 3. We multiply 2 and 3 vertically , get 6 as their product and put it down as the last right-hand-most part of the answer.

Thus 12 x 13 = 156

12 13 ___________ 1:3+2:6=156

Coming back to the problem at hand we need 28 x 28

Answer is (2*2+ carry forward from prev) : (2*8 +2*8+ carry forward from prev): ( 8x8)

There is one method that yields accurate results for all numbers. It is especialy applicable to numbers less than 30, you can solve their squares without paper. For numbers over 30 it requiers just one multiplication with multiples of 10 which is quite straightforward. Here we go:

97^2 = (97+7)*90 + 7^2
= 104*90 + 49
at this point you may need a paper and pencil, but calculation is very straightforward since you have to multiply 1040 with 9
= 9360 + 49 = 9409

The strongest points of this technique are its simplicity and ability to calculate even most complicated numbers, even 13 or 14 digit numbers which i have to doubt anyone will ever see on actual test.

There is one method that yields accurate results for all numbers. It is especialy applicable to numbers less than 30, you can solve their squares without paper. For numbers over 30 it requiers just one multiplication with multiples of 10 which is quite straightforward. Here we go:

97^2 = (97+7)*90 + 7^2 = 104*90 + 49 at this point you may need a paper and pencil, but calculation is very straightforward since you have to multiply 1040 with 9 = 9360 + 49 = 9409

The strongest points of this technique are its simplicity and ability to calculate even most complicated numbers, even 13 or 14 digit numbers which i have to doubt anyone will ever see on actual test.

Interesting ... Welcome to the GMATClub !

To me... well... I prefer to do 57 * 57 by the usual way of calculating by hand .... I mean I don't feel that I'm going less fast than by doing your technic