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(root(9 + root(80)) + root(9 - root(80)))^2 = [#permalink ]
02 Jan 2009, 17:42

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Question Stats:

68% (02:14) correct

32% (01:23) wrong

based on 105 sessions
(\sqrt{9+sqrt{80}}+\sqrt{9-\sqrt{80}})^2= A. 1

B. 9 - 4*5^1/2

C. 18 - 4*5^1/2

D. 18

E. 20

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Last edited by

Bunuel on 17 Apr 2014, 00:04, edited 1 time in total.

Renamed the topic, edited the question and added the OA.

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Re: Square root addition [#permalink ]
02 Jan 2009, 18:16

That's what I answered, but that is not the correct answer according to the GMATprep.

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Re: Square root addition [#permalink ]
03 Jan 2009, 15:10

9 + sqrt(80) + 9 -sqrt(80) + 2 sqrt (81-80) =20

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Re: Square root addition [#permalink ]
03 Jan 2009, 20:55

icandy, that is the correct answer, can you please explain your approach? thanks

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Re: Square root addition [#permalink ]
04 Jan 2009, 17:54

These are the concept that you need to know to solve this problem (x+y)^2 = x^2 +2xy+y^2 sqrtX times sqrt Y = sqrt XY (a-b)(a+b) = a^2-b^2

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Re: Square root addition [#permalink ]
05 Jan 2009, 16:55

(x+y)^2 = x^2+y^2+2xy 2*(9+sqrt(80))*(9-sqrt(80)=2*(81-80). Rest of the explanation is clear from icandy.

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Re: Square root addition [#permalink ]
10 Jan 2009, 10:46

squaring the term gives 9 + sqrt(80) + 9 - sqrt(80 + 2*(81 - 80) = 20

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Re: Square root addition [#permalink ]
31 Aug 2009, 04:27

nagk78 wrote:

squaring the term gives 9 + sqrt(80) + 9 - sqrt(80 + 2*(81 - 80) = 20

I understand the concept of x^2 + y^2 +2xy ...

But can someone please explain how in the part

2xy they are getting

2*(81-80) ?

Because

2xy is 2 * (

sqrt(9) + sqrt(80) *

sqrt(9) - sqrt(80) ) ...

or 2 * (sqrt(81)-sqrt(80))

i.e. not simply 81-80

**or is this one of those "find the closest approximation" questions.... and therefore should be spelled out in the question itself on the real GMAT?

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Re: Squares and Roots - PS [#permalink ]
31 Aug 2009, 14:54

(sqrt{a} + sqrt{b})^2 = a + b + 2*sqrt{ab} Here, a = 9 + sqrt{81} b = 9 - sqrt{81} therefore, answer = 9 + [strike]sqrt{81}[/strike] + 9 - [strike]sqrt{81}[/strike] + 2*(81-80) = 9 + 9 + 2 = 20

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Re: Squares and Roots - PS [#permalink ]
31 Aug 2009, 22:10
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i simply approximated

i know .... 4 sqrt(5) = 4 * 2.2 ~ 8.8

on simplyfying (a+b)^ 2 .....i get major terms as 2*9+2*...... = hence ans is more than 18 hence 20

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Re: Squares and Roots - PS [#permalink ]
14 Sep 2010, 23:30

im still not seeing the 81 and 80 here.....

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Re: Squares and Roots - PS [#permalink ]
14 Sep 2010, 23:36
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Re: Squares and Roots - PS [#permalink ]
15 Sep 2010, 01:26

Bunuel wrote:

djslobo wrote:

im still not seeing the 81 and 80 here.....

Hi and welcome to Gmat Club. Below is properly formated solution for this problem:

You should know two properties:

1.

(x+y)^2=x^2+2xy+y^2 , (

(x-y)^2=x^2-2xy+y^2 );

2.

(x+y)(x-y)=x^2-y^2 .

(\sqrt{9+sqrt{80}}+\sqrt{9-\sqrt{80}})^2=(\sqrt{9+\sqrt{80}})^2+2(\sqrt{9+\sqrt{80}})(\sqrt{9-sqrt{80}})+(\sqrt{9-\sqrt{80}})^2= =9+\sqrt{80}+2\sqrt{(9+\sqrt{80})(9-\sqrt{80})}+9-\sqrt{80}=18+2\sqrt{9^2-(\sqrt{80})^2}=18+2\sqrt{81-80}=18+2=20 .

Answer: E.

Hope it helps.

thnxs for the lucid explaination

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Re: Squares and Roots - PS [#permalink ]
16 Apr 2014, 19:14

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Re: Squares and Roots - PS
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16 Apr 2014, 19:14