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# is there a shortcut to quickly calculate a square of a

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CEO
Joined: 21 Jan 2007
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is there a shortcut to quickly calculate a square of a [#permalink]  15 May 2007, 21:38
is there a shortcut to quickly calculate a square of a number? let's say 28 squared...
Senior Manager
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i'd just multiply it 28*28 it's a pretty quick method
Manager
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there is no shortcut to success ..

but for few squares there is
9998^2

(10000-2)^2 now apply a^2+b^2-2*a*b

any other inputs
VP
Joined: 08 Jun 2005
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apache wrote:
there is no shortcut to success ..

but for few squares there is
9998^2

(10000-2)^2 now apply a^2+b^2-2*a*b

any other inputs

nice ! thanks apache.

Director
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Re: shortcut for squares? [#permalink]  15 May 2007, 23:28
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
CEO
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Re: shortcut for squares? [#permalink]  18 May 2007, 16:30
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.
Current Student
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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
Director
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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.....
Intern
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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)

which is (4+carry):(16+16+6):4
or (4+3):84
or 784
Attachments

File comment: Vedic Math - multiplication
Vedic_math_multiplication.doc [30 KiB]

VP
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wow !

thanks for sharing manish.gmat

http://tinyurl.com/3dzeyb

Director
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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)

which is (4+carry):(16+16+6):4
or (4+3):84
or 784

KillerSquirrel wrote:
wow !

thanks for sharing manish.gmat

http://tinyurl.com/3dzeyb

both are wonderful. thanks.
GMAT Forum Moderator
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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:

28^2 = (28+8)*20 + 8^2
= 36*20 + 64
= 720+64 = 784

Another example:

57^2 = (57+7)*50 + 7^2
= 64*50 + 49
= 3200 + 49 = 3249

And one more:

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.
SVP
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Pathfinder_77 wrote:
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:

28^2 = (28+8)*20 + 8^2
= 36*20 + 64
= 720+64 = 784

Another example:

57^2 = (57+7)*50 + 7^2
= 64*50 + 49
= 3200 + 49 = 3249

And one more:

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
VP
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All set and one one has to practice really hard to master the techniques. Other they may prove to counter your accuracy.
SVP
Joined: 29 Aug 2007
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Thanks everybody for your methods and certainly it is nice to know new methods of calculation.

I liked this one because it is easy to multiply integers by 100: 97^2
= (100-3)^2
= 100^2 - 2x100x3 + 3^2
= 10,000 - 600 + 9
= 9,400 + 9
= 9,409
CEO
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GMAT TIGER wrote:
Thanks everybody for your methods and certainly it is nice to know new methods of calculation.

I liked this one because it is easy to multiply integers by 100: 97^2
= (100-3)^2
= 100^2 - 2x100x3 + 3^2
= 10,000 - 600 + 9
= 9,400 + 9
= 9,409

http://www.gmatclub.com/forum/t55624
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# is there a shortcut to quickly calculate a square of a

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