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# Which of the following is equal to [1/([square_root]3[/squar

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Intern
Joined: 04 Aug 2010
Posts: 15
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Kudos [?]: 1 [0], given: 0

Which of the following is equal to [1/([square_root]3[/squar [#permalink]  04 Aug 2010, 02:56
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Difficulty:

25% (low)

Question Stats:

76% (01:37) correct 23% (01:22) wrong based on 26 sessions
Which of the following is equal to \frac{1}{(\sqrt{3}-\sqrt{2})^2.

A. 1
B. 5
C. \sqrt{6}
D. 5 - \sqrt{6}
E. 5 + 2\sqrt{6}
[Reveal] Spoiler: OA
Manager
Joined: 16 Apr 2010
Posts: 223
Followers: 3

Kudos [?]: 33 [0], given: 12

Re: Square root problem #1 [#permalink]  04 Aug 2010, 03:07
Hi,

[1/ (sqrt3-sqrt2)]^2 = [1/ (3+2 - 2sqrt6)] = (5 + 2sqrt6)/ (25-24) = 5 + 2sqrt6

regards,
Jack
Math Expert
Joined: 02 Sep 2009
Posts: 16995
Followers: 2787

Kudos [?]: 17752 [0], given: 2279

Re: Square root problem #1 [#permalink]  04 Aug 2010, 03:10
Expert's post
kwhitejr wrote:
Can anyone demonstrate the following?

Which of the following is equal to [1/(\sqrt{3} - \sqrt{2})]^2 ?

A. 1
B. 5
C. \sqrt{6}
D. 5 - \sqrt{6}
E. 5 + 2\sqrt{6}

Two things to know to deal with this problem (helps to rationalize):

1. (a-b)^2=a^2-2ab+b^2 and 2. (a-b)(a+b)=a^2-b^2.

\frac{1}{(\sqrt{3}-\sqrt{2})^2}=\frac{1}{3-2\sqrt{6}+2}=\frac{1}{5-2\sqrt{6}}. Now multiply both nominator and denominator by 5+2\sqrt{6} --> \frac{5+2\sqrt{6}}{(5-2\sqrt{6})(5+2\sqrt{6})}=\frac{5+2\sqrt{6}}{25-24}=5+2\sqrt{6}.

Hope it's clear.

 ! Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/No posting of PS/DS questions is allowed in the main Math forum.

_________________
Re: Square root problem #1   [#permalink] 04 Aug 2010, 03:10
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