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

It is currently 25 Oct 2014, 02:40

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

sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) =

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 15 Jul 2005
Posts: 106
Followers: 1

Kudos [?]: 4 [0], given: 0

sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) = [#permalink] New post 13 Sep 2005, 12:36
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:52) correct 0% (00:00) wrong based on 0 sessions
\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} =
VP
VP
avatar
Joined: 22 Aug 2005
Posts: 1128
Location: CA
Followers: 1

Kudos [?]: 32 [0], given: 0

 [#permalink] New post 13 Sep 2005, 13:14
(sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3))

multiple both numerator and denominator by :
(sqrt(5)+sqrt(3))

gives:

{[(sqrt(5)+sqrt(3))] ^ 2} / 2

or

4 + sqrt (15)
Manager
Manager
avatar
Joined: 15 Jul 2005
Posts: 106
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 13 Sep 2005, 19:34
the reason i posted this question was to ask a second question.

if you chose to multiply the numerator and denominator by sqrt(5)+sqrt(3) you get 4+sqrt(5)*sqrt(3)

though, if you chose to multiply the numerator and denominator by sqrt(5)-sqrt(3) you get 1 / (4-sqrt(5)*sqrt(3))

though seemingly different,

4+sqrt(5)*sqrt(3) = 1/(4-sqrt(5)*sqrt(3))

I am not sure whether there is a broad generalization i am missing. If anyone can shed light on this, that would be great!
Senior Manager
Senior Manager
User avatar
Joined: 14 Apr 2005
Posts: 422
Location: India, Chennai
Followers: 1

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

Re: Easy PS: [#permalink] New post 13 Sep 2005, 22:56
chets wrote:
(sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) = ?


Take conjugate on both sides. which gives.

(sqrt(5) + sqrt(3)) (sqrt(5) + sqrt(3)) / (sqrt(5) - sqrt(3)) (sqrt(5) + sqrt(3))

This gives (sqrt(5) +sqrt(3))^2 / (Sqrt(5)^2) - (sqrt(3))^2

=> 5 + 3 + 2 sqrt(15) / 2

=> 2(4 + sqrt(15))/2

=> 4 + sqrt(15)

Thanks
Senior Manager
Senior Manager
avatar
Joined: 22 Jun 2005
Posts: 364
Location: London
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 14 Sep 2005, 05:34
chets wrote:
the reason i posted this question was to ask a second question.

if you chose to multiply the numerator and denominator by sqrt(5)+sqrt(3) you get 4+sqrt(5)*sqrt(3)

though, if you chose to multiply the numerator and denominator by sqrt(5)-sqrt(3) you get 1 / (4-sqrt(5)*sqrt(3))

though seemingly different,

4+sqrt(5)*sqrt(3) = 1/(4-sqrt(5)*sqrt(3))

I am not sure whether there is a broad generalization i am missing. If anyone can shed light on this, that would be great!



Chet,

You r not missing anything,

You get:

1/(4-sqrt(5)*sqrt(3)) =


(4+sqrt(5)*sqrt(3)) / [(4-sqrt(5)*sqrt(3))(4+sqrt(5)*sqrt(3))] =


(4+sqrt(5)*sqrt(3)) / (16 - 15) =


(4+sqrt(5)*sqrt(3))

Hope that helps :)
Intern
Intern
User avatar
Joined: 14 May 2014
Posts: 45
Followers: 0

Kudos [?]: 18 [0], given: 1

Re: sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) = [#permalink] New post 21 May 2014, 07:38
This type of questions can be solved by using formula

(a+b)(a-b) = a^2 - b^2

Denominator is in the form of a-b , hence we will multiply numerator and denominator by the form a +b .i.e. sqrt(5) + sqrt(3)

sqrt(5) + sqrt(3)/sqrt(5) - sqrt(3)

[sqrt(5) + sqrt(3)]*[sqrt(5) + sqrt(3)]/[sqrt(5) + sqrt(3)]*[sqrt(5) - sqrt(3)]

5+3 + 2*sqrt(5)*sqrt(3) / 5-3

8+2*sqrt(5)*sqrt(3)/2

4+sqrt(15)
_________________

Help me with Kudos if it helped you "

Mathematics is a thought process.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28940 [0], given: 2871

Re: sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) = [#permalink] New post 22 May 2014, 02:33
Expert's post
chets wrote:
\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} =


Similar questions to practice:
sum-of-the-series-86458.html
if-x-0-then-106291.html
if-n-is-positive-which-of-the-following-is-equal-to-31236.html
sqrt-15-4-sqrt-14-sqrt-15-4-sqrt-146872.html
if-x-is-positive-then-1-root-x-1-root-x-163491.html
which-of-the-following-is-equal-to-3-squar-98531.html

Theory on roots problems: math-number-theory-88376.html

All DS roots problems to practice: search.php?search_id=tag&tag_id=49
All PS roots problems to practice: search.php?search_id=tag&tag_id=113

Tough and tricky exponents and roots questions (DS): tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky exponents and roots questions (PS): new-tough-and-tricky-exponents-and-roots-questions-125956.html

_________________

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

Intern
Intern
avatar
Joined: 19 May 2014
Posts: 31
Followers: 0

Kudos [?]: 3 [0], given: 6

Re: sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) = [#permalink] New post 22 May 2014, 13:59
Chets asked if 4+sqrt(5)*sqrt(3) = 1/(4-sqrt(5)*sqrt(3)) can be extrapolated into a broad generalization. No, it can't be!

Here's why.

Consider an expression 1/(a-\sqrt{bc}) [modeled on 1/(4-sqrt(5)*sqrt(3)) ]
Multiplying Numerator and Denominator with (a+ \sqrt{bc}), we get
(a+ \sqrt{bc})/(a^2-bc)

So, the reason why 1/(4-sqrt(5)*sqrt(3) got simplified into 4+sqrt(5)*sqrt(3) was because the Denominator of the above expression is equal to 1 in this particular case (a=4, b=5, c=3. So,a^2-bc = 4^2-5*3 = 1)
_________________

Please press Kudos if you were helped by my post!

VP
VP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1088
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 6

Kudos [?]: 308 [0], given: 170

Re: sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) = [#permalink] New post 22 May 2014, 18:37
Multiply numerator & denominator by (\sqrt{5} + \sqrt{3})

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

= \frac{5 + 2\sqrt{15} + 3}{5 - 3}

= \frac{8 + 2\sqrt{15}}{2}

= 4 + \sqrt{15}

Formulae used:

(a+b)^2 = a^2 + 2ab + b^2

(a-b)^2 = a^2 - b^2

_________________

Kindly press "+1 Kudos" to appreciate :)

Re: sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) =   [#permalink] 22 May 2014, 18:37
Display posts from previous: Sort by

sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) =

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.