Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2] : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 Feb 2017, 09:22

# LIVE NOW:

Cornell Johnson Adcoms on GMATClub to Chat with Applicants - Join Chat Room to Participate

### 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

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

# 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]

Author Message
TAGS:

### Hide Tags

Intern
Joined: 04 Aug 2010
Posts: 14
Followers: 0

Kudos [?]: 46 [0], given: 0

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

### Show Tags

04 Aug 2010, 02:56
2
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

75% (02:09) correct 25% (01:17) wrong based on 279 sessions

### HideShow timer Statistics

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: 221
Followers: 4

Kudos [?]: 121 [0], given: 12

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

### Show Tags

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: 37154
Followers: 7279

Kudos [?]: 96872 [0], given: 10808

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

### Show Tags

04 Aug 2010, 03:10
Expert's post
4
This post was
BOOKMARKED
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.

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 50

Kudos [?]: 1994 [1] , given: 193

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

### Show Tags

22 May 2014, 19:22
1
KUDOS
Multiply both numerator & denominator by $$(\sqrt{3} + \sqrt{2})^2$$

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

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

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

$$= 5 + 2\sqrt{6}$$

_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14004
Followers: 592

Kudos [?]: 168 [0], given: 0

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

### Show Tags

28 Dec 2016, 03:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Which of the following is equal to 1/[(3^(1/2)-2^(1/2))^1/2]   [#permalink] 28 Dec 2016, 03:08
Similar topics Replies Last post
Similar
Topics:
2 14! is equal to which of the following? 9 20 Apr 2016, 00:04
6^6 is equal to which of the following? 7 14 Apr 2016, 01:32
2 Which of the following is equal to 8 28 Jun 2013, 22:12
Which of the following is equal to the average (arithmetic 8 16 Jun 2012, 19:42
6 If n is positive, which of the following is equal to 5 05 Nov 2008, 20:26
Display posts from previous: Sort by