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

It is currently 20 Oct 2019, 02:27

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.

Close

Request Expert Reply

Confirm Cancel

(1+ (3)^1/3) (2+(3^1/2))^1/2?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 18 Apr 2013
Posts: 33
(1+ (3)^1/3) (2+(3^1/2))^1/2?  [#permalink]

Show Tags

New post Updated on: 03 Oct 2017, 02:16
17
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

49% (02:23) correct 51% (02:41) wrong based on 182 sessions

HideShow timer Statistics

\((1+ \sqrt{3})*(\sqrt{2+\sqrt{3}})\)


A. \(\sqrt{2}(2+\sqrt{3})\)

B. \(\sqrt{2}(3+\sqrt{3})\)

C. \(\sqrt{2}(2-\sqrt{3})\)

D. \(\sqrt{3}(2+\sqrt{3})\)

E. \(\sqrt{2}(2+\sqrt{2})\)

Attachment:
Capture.JPG
Capture.JPG [ 17.72 KiB | Viewed 2468 times ]

Originally posted by roastedchips on 06 Jul 2017, 07:18.
Last edited by Bunuel on 03 Oct 2017, 02:16, edited 2 times in total.
Formatted the question.
Most Helpful Community Reply
Current Student
User avatar
B
Joined: 09 Dec 2015
Posts: 112
Location: India
Concentration: General Management, Operations
Schools: IIMC (A)
GMAT 1: 700 Q49 V36
GPA: 3.5
WE: Engineering (Consumer Products)
Reviews Badge
Re: (1+ (3)^1/3) (2+(3^1/2))^1/2?  [#permalink]

Show Tags

New post 10 Jul 2017, 09:29
8
1
Easy method,
Let (1+√3)√(2+√3) = x. Square both sides
x^2 = (1+√3)^2 * (2+√3)
= (1 + 3 + 2√3) * (2 + √3)
= (4 + 2√3) * (2 + √3)
= 2(2 + √3) * (2 + √3)
= 2 * (2 + √3)^2.
Take square root of both sides, x = √2 * (2 + √3)
General Discussion
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
(1+ (3)^1/3) (2+(3^1/2))^1/2?  [#permalink]

Show Tags

New post 06 Jul 2017, 08:20
3
2
Let X = \((1+ \sqrt{3})\sqrt{(2+3^{1/2})}\) = \((1+ \sqrt{3})\sqrt{(1 + 1 + 3^{1/2})}\)

If a = \(1+ \sqrt{3}\), then \(a^2 = 1 + 3 + 2\sqrt{3} = 4 + 2\sqrt{3}\)

The expression now becomes X = \(a * \sqrt{1 + a}\)

Squaring, we get \(X^2 = a^2(1+a)\)

Substituting values, \(X^2 = (4 + 2\sqrt{3})(2 + \sqrt{3}) = 2(2 + \sqrt{3})(2 + \sqrt{3})\)

Taking square root, we have X = \(\sqrt{2}(2 + \sqrt{3})\) (Option A)
_________________
You've got what it takes, but it will take everything you've got
Intern
Intern
avatar
B
Joined: 10 May 2018
Posts: 47
(1+ (3)^1/3) (2+(3^1/2))^1/2?  [#permalink]

Show Tags

New post 02 Mar 2019, 13:17
1
OhsostudiousMJ

Squaring the expression = (1+3+2√3)(2+√3)
=2+√3+6+3√3+4√3+6
=14+8√3 (..At this point I'm pretty sure that Im going the wrong way.)
=6+8+8√3
=6+8(1+√3

==> 14 +8√3
=8 +6+4√3 +4√3
=4(2+√3) +2√3(2+√3)
=(4+2√3)(2+√3)
=2(2+√3) (2+√3)
=2(2+√3)^2
x =√2(2+√3)
Manager
Manager
avatar
B
Joined: 04 May 2014
Posts: 151
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: (1+ (3)^1/3) (2+(3^1/2))^1/2?  [#permalink]

Show Tags

New post 27 Sep 2017, 09:10
pushpitkc wrote:
Let X = \((1+ \sqrt{3})\sqrt{(2+3^{1/2})}\) = \((1+ \sqrt{3})\sqrt{(1 + 1 + 3^{1/2})}\)

If a = \(1+ \sqrt{3}\), then \(a^2 = 1 + 3 + 2\sqrt{3} = 4 + 2\sqrt{3}\)

The expression now becomes X = \(a * \sqrt{1 + a}\)

Squaring
\(X^2 = a^2(1+a)\)

Substituting values,
\(X^2 = (4 + 2\sqrt{3})(2 + \sqrt{3})\)
\(= 2(2 + \sqrt{3})(2 + \sqrt{3})\)

Taking square root
X = \(\sqrt{2}(2 + \sqrt{3})\) (Option A)



Are we allowed to take 2 common from one bracket set?

eg 6X7=2(3)(7)
Current Student
User avatar
B
Joined: 09 Dec 2015
Posts: 112
Location: India
Concentration: General Management, Operations
Schools: IIMC (A)
GMAT 1: 700 Q49 V36
GPA: 3.5
WE: Engineering (Consumer Products)
Reviews Badge
Re: (1+ (3)^1/3) (2+(3^1/2))^1/2?  [#permalink]

Show Tags

New post 03 Oct 2017, 00:16
gps5441 wrote:
pushpitkc wrote:
Let X = \((1+ \sqrt{3})\sqrt{(2+3^{1/2})}\) = \((1+ \sqrt{3})\sqrt{(1 + 1 + 3^{1/2})}\)

If a = \(1+ \sqrt{3}\), then \(a^2 = 1 + 3 + 2\sqrt{3} = 4 + 2\sqrt{3}\)

The expression now becomes X = \(a * \sqrt{1 + a}\)

Squaring
\(X^2 = a^2(1+a)\)

Substituting values,
\(X^2 = (4 + 2\sqrt{3})(2 + \sqrt{3})\)
\(= 2(2 + \sqrt{3})(2 + \sqrt{3})\)

Taking square root
X = \(\sqrt{2}(2 + \sqrt{3})\) (Option A)



Are we allowed to take 2 common from one bracket set?

eg 6X7=2(3)(7)


Yes you can take '2' common from one braket.

Notice that when you multiply '2' back to the braket, you'll get the previous equation.

I'll explain with example.

Case 1: Let us say an equation is x = (2y + 4)*(y^2 + 3y); here x and y are some variables.
In this case you can take '2' common from first bracket and 'y' common from second bracket. Equation can be written as, x = 2y*(y+2)*(y+3).
You can also multiply '2' and 'y' separately to the brackets, even to the bracket from which each was not taken.
Equation can also be written as, x = (y^2+2y)*(2y+6) = 2*(y^2+2y)*(y+3) = y*(y+2)*(2y+6). All these equations are same and correct.

Case 2: Let us say an equation is x = (2y + 4) + (y^2 + 3y); here x and y are some variables.
In this case also you can take '2' common from first bracket and 'y' common from second bracket but you cannot multiply both commons like in previous case.
Equation will be written as, x = 2(y+2) + y(y+3). This equation is same as original equation.

Case 3: Let us say an equation is x = (3y + 6) + (y^2 + 2y); here x and y are some variables.
In this case also you can take '2' common from first bracket and 'y' common from second bracket. Equation can be written as, x = 3(y+2)+y(y+2).
In this case, you can take '(y+2)' as common and equation will become, x = (y+2)*(y+3).

I hope this clears your doubt.
Intern
Intern
avatar
Joined: 31 Aug 2017
Posts: 1
Re: (1+ (3)^1/3) (2+(3^1/2))^1/2?  [#permalink]

Show Tags

New post 03 Oct 2017, 02:15
Very informative thread.
Manager
Manager
avatar
S
Joined: 28 Jan 2019
Posts: 97
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
WE: Manufacturing and Production (Manufacturing)
Re: (1+ (3)^1/3) (2+(3^1/2))^1/2?  [#permalink]

Show Tags

New post 01 Mar 2019, 04:13
Hey can someone help me out here pls.. here's where I'm stuck.

Squaring the expression = (1+3+2√3)(2+√3)
=2+√3+6+3√3+4√3+6
=14+8√3 (..At this point I'm pretty sure that Im going the wrong way.)
=6+8+8√3
=6+8(1+√3)
=??
_________________
"Luck is when preparation meets opportunity!"
GMAT Club Bot
Re: (1+ (3)^1/3) (2+(3^1/2))^1/2?   [#permalink] 01 Mar 2019, 04:13
Display posts from previous: Sort by

(1+ (3)^1/3) (2+(3^1/2))^1/2?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne