GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Nov 2018, 19:44

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# root[3*root{80}+3/(9+4*root{5})]=?

Author Message
TAGS:

### Hide Tags

Director
Joined: 03 Sep 2006
Posts: 793

### Show Tags

26 Jan 2012, 05:30
6
00:00

Difficulty:

35% (medium)

Question Stats:

71% (02:07) correct 29% (02:33) wrong based on 432 sessions

### HideShow timer Statistics

$$\sqrt{3*\sqrt{80}+\frac{3}{9+4*\sqrt{5}}}=?$$

A) $$\sqrt{3*\sqrt{5}}$$

B) 3

C) $$3*\sqrt{3}$$

D) $$3+2*\sqrt{5}$$

E) $$9+4*\sqrt{5}$$
Math Expert
Joined: 02 Sep 2009
Posts: 50627

### Show Tags

26 Jan 2012, 05:59
5
4
LM wrote:
$$\sqrt{3*\sqrt{80}+\frac{3}{9+4*\sqrt{5}}}=?$$

A) $$\sqrt{3*\sqrt{5}}$$

B) 3

C) $$3*\sqrt{3}$$

D) $$3+2*\sqrt{5}$$

E) $$9+4*\sqrt{5}$$

$$\sqrt{3\sqrt{80}+\frac{3}{9+4\sqrt{5}}}=\sqrt{12\sqrt{5}+\frac{3}{9+4\sqrt{5}}*\frac{9-4\sqrt{5}}{9-4\sqrt{5}}}=\sqrt{12\sqrt{5}+\frac{3(9-4\sqrt{5})}{81-80}}=\sqrt{12\sqrt{5}+27-12\sqrt{5}}=\sqrt{27}=3\sqrt{3}$$.

_________________
##### General Discussion
Manager
Joined: 22 Mar 2012
Posts: 85
Location: United States (NY)
Concentration: General Management, Marketing
GPA: 3.1
WE: Accounting (Other)

### Show Tags

12 Aug 2012, 08:56
Thanks Bunuel -- You Are The Man!!
Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 198
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)

### Show Tags

12 Aug 2012, 10:29
This can be solved by taking the denominator as 9+4\sqrt{5} and then taking this as the common factor. We get the the ans as C.
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Manager
Joined: 28 Feb 2012
Posts: 112
GPA: 3.9
WE: Marketing (Other)

### Show Tags

16 Aug 2012, 22:16
This kind of problems always seemed to me very scary and requires a lot of calculation, but later i realised that GMAT never asks something that you need to calculate a lot, so one needs to look for some pattern or similar numbers/sets. In our case, we look at denominator 9+\sqrt{5} and 3\sqrt{80}, so 80 is 2^4*5, which means 4\sqrt{5}, from here we feel that numerator and denominator could be reduced. The rest is just calculations. In my opinion the most crucial part is this one.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1073
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: Que from MGMAT -  [#permalink]

### Show Tags

07 Apr 2013, 10:07
Lets analyze the first part $$3\sqrt{80} = 3\sqrt{5*16} = 3*4\sqrt{5}$$
The second term: Denominator $$(9+4\sqrt{5})*(9-4\sqrt{5})=9^2-4^2*5=1$$ Rule: (x+y)(x-y)=x^2-y^2
The second term: Numerator $$3*(9-4\sqrt{5})=27-12\sqrt{5}$$
Now putting all in one:
$$\sqrt{(}12\sqrt{5}+27-12\sqrt{5})=$$
$$\sqrt{27}=\sqrt{3*3^2}=3\sqrt{3}$$

Hope it's clear now
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1826
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

### Show Tags

02 Jan 2015, 00:12
$$\sqrt{3*\sqrt{80}+\frac{3}{9+4*\sqrt{5}}}$$

$$= \sqrt{3 * (4\sqrt{5}+\frac{1}{9+4*\sqrt{5}})}$$

$$= \sqrt{3 * \frac{36\sqrt{5} + 80 + 1}{9+4*\sqrt{5}}}$$

$$= \sqrt{3 * 9 * \frac{9+4*\sqrt{5}}{9+4*\sqrt{5}}}$$

$$= 3 \sqrt{3}$$
_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 20 Mar 2015
Posts: 1

### Show Tags

04 Apr 2015, 06:52
2
1
LM wrote:
$$\sqrt{3*\sqrt{80}+\frac{3}{9+4*\sqrt{5}}}=?$$

A) $$\sqrt{3*\sqrt{5}}$$

B) 3

C) $$3*\sqrt{3}$$

D) $$3+2*\sqrt{5}$$

E) $$9+4*\sqrt{5}$$

Though, I am quite comfortable with the method mentioned by Bunuel, I found an alternative way by The Economist.

$$9 + 4*\sqrt{5}$$ will be approx. equal to 9 + 4 x 2 = 17. Hence 3/ 17 will be quite less to contribute towards the value of expression.

$$3\sqrt{80}$$ is approx. 3 x 9 = 27. now $$\sqrt{27}$$ will be something more than 5.

Now coming to options:

(A)$$\sqrt{3*\sqrt{5}}$$ is approx $$\sqrt{6}$$ which is quite less than 5. Rejected.
(B) Rejected.
(C) 3 x 1.732 = 5.1 , which is in our desired range.
(D) 3 + 4 =7. Rejected
(E) 9 + 4 x 2 = 17. Rejected.

Hence the correct ans is (C).

If you like this Ballparking method, please press "Kudos".
Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 378

### Show Tags

27 Oct 2016, 18:41
Multiplying by the conjugate is the trick for this problem.

[3/(9+4sqrt(5))][(9-4sqrt(5)/9-4sqrt(5)] = 27-12sqrt(5)

sqrt(80) = 4sqrt(5)

Plug into equation 12sqrt(5) cancels out and we are left with sqrt(27) = 3sqrt(3)
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

### Show Tags

12 Nov 2017, 07:30
LM wrote:
$$\sqrt{3*\sqrt{80}+\frac{3}{9+4*\sqrt{5}}}=?$$

A) $$\sqrt{3*\sqrt{5}}$$

B) 3

C) $$3*\sqrt{3}$$

D) $$3+2*\sqrt{5}$$

E) $$9+4*\sqrt{5}$$

Let’s first simplify 3√80:

3√80 = 3 x √16 x √5 = 12√5

Next, let’s simplify 3/(9 + 4√5) by rationalizing the denominator:

3/(9 + 4√5) x (9 - 4√5)/(9 - 4√5) = (27 - 12√5)/(81 - 80) = 27 - 12√5

Finally, we have:

√(12√5 + 27 - 12√5) = √27 = √9 x √3 = 3√3

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: root[3*root{80}+3/(9+4*root{5})]=? &nbs [#permalink] 12 Nov 2017, 07:30
Display posts from previous: Sort by