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# GMAT Prep Radicals and Exponents operations question

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Manager
Joined: 06 Jan 2008
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GMAT Prep Radicals and Exponents operations question [#permalink]

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04 Oct 2009, 13:48
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Can't figure out hwo to get this one to show up using html tags...

so i'll try it with text:

[(radical(9+radical(80)) + (radical(9-radical(80)) ] ^ 2 = ???

Kudos [?]: 119 [0], given: 1

Manager
Joined: 11 Sep 2009
Posts: 129

Kudos [?]: 413 [1], given: 6

Re: GMAT Prep Radicals and Exponents operations question [#permalink]

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04 Oct 2009, 14:42
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The answer is 20.

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

$$= (\sqrt{9+\sqrt{80}} + \sqrt{9-\sqrt{80}})(\sqrt{9+\sqrt{80}} + \sqrt{9-\sqrt{80}})$$

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

$$= 18 + 2\sqrt{9^2-\sqrt{80}^2}$$

$$= 18 + 2\sqrt{1}$$

$$= 20$$

Kudos [?]: 413 [1], given: 6

Founder
Joined: 04 Dec 2002
Posts: 15456

Kudos [?]: 27965 [0], given: 5052

Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: GMAT Prep Radicals and Exponents operations question [#permalink]

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07 Oct 2009, 21:45
Here is the code of the Math Tags:

Code:
The answer is [b]20[/b].

[m](\sqrt{9+\sqrt{80}} + \sqrt{9-\sqrt{80}})^2[/m]

[m]= (\sqrt{9+\sqrt{80}} + \sqrt{9-\sqrt{80}})(\sqrt{9+\sqrt{80}} + \sqrt{9-\sqrt{80}})[/m]

[m]= (9+\sqrt{80}) + 2\sqrt{9+\sqrt{80}}\sqrt{9-\sqrt{80}} + (9-\sqrt{80})[/m]

[m]= 18 + 2\sqrt{9^2-\sqrt{80}^2}[/m]

[m]= 18 + 2\sqrt{1}[/m]

[m]= 20[/m]

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Kudos [?]: 27965 [0], given: 5052

Manager
Joined: 18 Jul 2009
Posts: 168

Kudos [?]: 114 [0], given: 37

Location: India
Schools: South Asian B-schools
Re: GMAT Prep Radicals and Exponents operations question [#permalink]

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07 Oct 2009, 22:43
Agree with AKProdigy87....20 it is
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Bhushan S.
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Re: GMAT Prep Radicals and Exponents operations question   [#permalink] 07 Oct 2009, 22:43
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# GMAT Prep Radicals and Exponents operations question

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