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(root(9 + root(80)) + root(9 - root(80)))^2 =

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(root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post Updated on: 29 Jul 2015, 00:00
3
13
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:37) correct 36% (02:05) wrong based on 551 sessions

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\((\sqrt{9+\sqrt{80}}+\sqrt{9-\sqrt{80}})^2=\)

A. 1
B. 9 - 4*5^1/2
C. 18 - 4*5^1/2
D. 18
E. 20

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Originally posted by smarinov on 02 Jan 2009, 17:42.
Last edited by Bunuel on 29 Jul 2015, 00:00, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 14 Sep 2010, 23:36
7
6
djslobo wrote:
im still not seeing the 81 and 80 here..... :cry:


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.
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Re: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 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: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 03 Jan 2009, 15:10
9 + sqrt(80) + 9 -sqrt(80) + 2 sqrt (81-80)

=20
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Re: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 03 Jan 2009, 20:55
icandy, that is the correct answer, can you please explain your approach?

thanks
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Re: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 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: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 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: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 10 Jan 2009, 10:46
squaring the term gives

9 + sqrt(80) + 9 - sqrt(80 + 2*(81 - 80) = 20
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Re: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 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: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 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: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 31 Aug 2009, 22:10
1
1
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: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 14 Sep 2010, 23:30
im still not seeing the 81 and 80 here..... :cry:
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Re: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 15 Sep 2010, 01:26
Bunuel wrote:
djslobo wrote:
im still not seeing the 81 and 80 here..... :cry:


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: (root(9 + root(80)) + root(9 - root(80)))^2 =  [#permalink]

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New post 05 Sep 2018, 09:41
If you are pressed for time on this question you can get down to D or E quickly by estimating. Convert the radicals to actual numbers and execute the arithmetic.

The answer choices are approximately
A 1
B ~0
C ~9
D 18
E 20

The question can be restated as

(sqrt(9+9) + sqrt (9-9))squared
sqrt(18)squared
18ish
D or E

Depending on your ability to execute the exponent algebra, it may be a "win" to get this quickly to a coin flip and move on.
A similar approach is useful on OG2019 77 (estimating the value of sqrt 2 and defining the longest and the shortest the cord could be), 81, 100, 119, and 180. 100 and 180 also need a variables in the answer choices approach.

Jayson Beatty
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Re: (root(9 + root(80)) + root(9 - root(80)))^2 = &nbs [#permalink] 05 Sep 2018, 09:41
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