Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 15:00

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2]

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 04 Aug 2010
Posts: 15
Followers: 0

Kudos [?]: 3 [0], given: 0

Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2] [#permalink] New post 04 Aug 2010, 02:56
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (02:11) correct 23% (01:08) wrong based on 91 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
Manager
avatar
Joined: 16 Apr 2010
Posts: 223
Followers: 3

Kudos [?]: 44 [0], given: 12

GMAT Tests User
Re: Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2] [#permalink] New post 04 Aug 2010, 03:07
Hi,

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

regards,
Jack
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24397 [0], given: 2677

Re: Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2] [#permalink] New post 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}.

Answer: E.

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.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 799
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 4

Kudos [?]: 194 [0], given: 164

Re: Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2] [#permalink] New post 22 May 2014, 19:22
Multiply both numerator & denominator by (\sqrt{3} + \sqrt{2})^2

= \frac{(\sqrt{3} + \sqrt{2})^2}{ (\sqrt{3} - \sqrt{2})^2 (\sqrt{3} + \sqrt{2})^2}

= \frac{3 + 2\sqrt{6} + 2 }{((\sqrt{3} - \sqrt{2}) (\sqrt{3} + \sqrt{2}))^2}

= \frac{5 + 2\sqrt{6}}{ (3 - 2)^2}

= 5 + 2\sqrt{6}

Answer = E
_________________

Kindly press "+1 Kudos" to appreciate :)

Re: Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2]   [#permalink] 22 May 2014, 19:22
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Which of the following is equal to fozzzy 7 28 Jun 2013, 22:12
Which of the following is equal to the value of smarinov 2 24 Dec 2008, 15:12
If n is positive, which of the following is equal to cejismundo 4 31 Aug 2006, 14:11
7 Experts publish their posts in the topic If n is positive, which of the following is equal to kook44 18 28 Jun 2006, 05:36
Which of the following is equal to value of jlui4477 5 17 Apr 2006, 00:43
Display posts from previous: Sort by

Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2]

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.