NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 21:47 It is currently 25 Apr 2024, 21:47
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Which of the following is equal to (2^3√3/√2)^3?

SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
B
bgbeidas
Manager
Manager
Joined: 01 Dec 2015
Posts: 109
Own Kudos [?]: 155 [101]
Given Kudos: 2
Location: Lebanon
Schools: LBS '19 (A) CBS '20 (S) Booth '20 (D)
GMAT 1: 760 Q49 V46
GPA: 2.99
Send PM
Reviews Badge
Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   13 Apr 2016, 01:33
5
Kudos
96
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

73% (01:21) correct 27% (01:42) wrong based on 1924 sessions
Hide Show timer Statistics
Which of the following is equal to \((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)?

A) 3√2/2
B) 3√2
C) 6√2
D) 12
E) 12√2
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4689 [19]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   13 Apr 2016, 12:50
17
Kudos
2
Bookmarks
bgbeidas wrote:

=>\((\sqrt{2}*\sqrt[3]{3})^3\)
=> \(2\sqrt{2}*3 = 6\sqrt{2}\)
C

I understand how you got 3, and how you should gt 2\sqrt{2} at the bottom.
But the 2 in the top part, when I cube it I get 8, not sure where that disappears in your process.



I think u are clear with this part =>\((\sqrt{2}*\sqrt[3]{3})^3\)

=>\((\sqrt{2}*\sqrt[3]{3})^3\)

=> (\(2^{1/2}\) * \(3^{1/3}\))\(^{3}\)

=> \(2^{3/2}\)* \(3^{3/3}\)

=>\(2^1\)* \(2^{1/2}\)* \(3^1\) { Because \(\frac{3}{2}\) = \(1 \frac{1}{2}\) and \(\frac{3}{3}\) = 1 }

=> \(2^1\)* \(2^{1/2}\)* \(3^1\)

=> 2*\(\sqrt{2}\) * 3

=>6\(\sqrt{2}\)


Hope this helps !! :-D :-D
avatar
AfricanPrincess
Intern
Intern
Joined: 20 Oct 2014
Posts: 3
Own Kudos [?]: 12 [12]
Given Kudos: 1
Send PM
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   06 Aug 2016, 08:25
12
Kudos
The way the question has been asked is ambiguous because of what looks like 2^3 in the numerator.

Posted from my mobile device
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31934 [10]
Given Kudos: 290
Send PM
Reviews Badge
Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   13 Apr 2016, 04:45
6
Kudos
3
Bookmarks
Expert Reply
bgbeidas wrote:
Not sure I fully understood your explanation to the question, is Bunuel around at all?



since thesee are standard number properties, even Bunuel will have to explain exactly what has been written ..
But may be I'll write it in detail..
\((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)

Substitute the values as following as-
\(2= \sqrt{2}*\sqrt{2}\)...
\(and 3= \sqrt[3]{3}*\sqrt[3]{3}*\sqrt[3]{3}\)...
\(2\sqrt{2}= \sqrt{2}*\sqrt{2}*\sqrt{2}\)...


=>\((\sqrt{2}*\sqrt[3]{3})^3\)
=> \(2\sqrt{2}*3 = 6\sqrt{2}\)
C
General Discussion
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31934 [11]
Given Kudos: 290
Send PM
Reviews Badge
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   13 Apr 2016, 02:39
6
Kudos
5
Bookmarks
Expert Reply
bgbeidas wrote:
Apologies in advance for the poor formatting, it's my first time posting a question on here.

Which of the following is equal to (2^3√3/√2)^3?

A) 3√2/2
B) 3√2
C) 6√2
D) 12
E) 12√2

If anyone looking to edit the question can't interpret the above please let me know.



Hi,

i believe the Q is meant to be..
\((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)
=>\((\sqrt{2}*\sqrt[3]{3})^3\)
=> \(2\sqrt{2}*3 = 6\sqrt{2}\)
C
avatar
B
bgbeidas
Manager
Manager
Joined: 01 Dec 2015
Posts: 109
Own Kudos [?]: 155 [0]
Given Kudos: 2
Location: Lebanon
Schools: LBS '19 (A) CBS '20 (S) Booth '20 (D)
GMAT 1: 760 Q49 V46
GPA: 2.99
Send PM
Reviews Badge
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   13 Apr 2016, 04:33
Not sure I fully understood your explanation to the question, is Bunuel around at all?
avatar
B
bgbeidas
Manager
Manager
Joined: 01 Dec 2015
Posts: 109
Own Kudos [?]: 155 [0]
Given Kudos: 2
Location: Lebanon
Schools: LBS '19 (A) CBS '20 (S) Booth '20 (D)
GMAT 1: 760 Q49 V46
GPA: 2.99
Send PM
Reviews Badge
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   13 Apr 2016, 07:28
chetan2u wrote:
bgbeidas wrote:
Not sure I fully understood your explanation to the question, is Bunuel around at all?



since thesee are standard number properties, even Bunuel will have to explain exactly what has been written ..
But may be I'll write it in detail..
\((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)

Substitute the values as following as-
\(2= \sqrt{2}*\sqrt{2}\)...
\(and 3= \sqrt[3]{3}*\sqrt[3]{3}*\sqrt[3]{3}\)...
\(2\sqrt{2}= \sqrt{2}*\sqrt{2}*\sqrt{2}\)...


=>\((\sqrt{2}*\sqrt[3]{3})^3\)
=> \(2\sqrt{2}*3 = 6\sqrt{2}\)
C



I understand how you got 3, and how you should gt 2\sqrt{2} at the bottom.
But the 2 in the top part, when I cube it I get 8, not sure where that disappears in your process.
avatar
B
bgbeidas
Manager
Manager
Joined: 01 Dec 2015
Posts: 109
Own Kudos [?]: 155 [1]
Given Kudos: 2
Location: Lebanon
Schools: LBS '19 (A) CBS '20 (S) Booth '20 (D)
GMAT 1: 760 Q49 V46
GPA: 2.99
Send PM
Reviews Badge
Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   13 Apr 2016, 23:47
1
Bookmarks
Abhishek009 wrote:
bgbeidas wrote:

=>\((\sqrt{2}*\sqrt[3]{3})^3\)
=> \(2\sqrt{2}*3 = 6\sqrt{2}\)
C

I understand how you got 3, and how you should gt 2\sqrt{2} at the bottom.
But the 2 in the top part, when I cube it I get 8, not sure where that disappears in your process.



I think u are clear with this part =>\((\sqrt{2}*\sqrt[3]{3})^3\)

=>\((\sqrt{2}*\sqrt[3]{3})^3\)

=> (\(2^{1/2}\) * \(3^{1/3}\))\(^{3}\)

=> \(2^{3/2}\)* \(3^{3/3}\)

=>\(2^1\)* \(2^{1/2}\)* \(3^1\) { Because \(\frac{3}{2}\) = \(1 \frac{1}{2}\) and \(\frac{3}{3}\) = 1 }

=> \(2^1\)* \(2^{1/2}\)* \(3^1\)

=> 2*\(\sqrt{2}\) * 3

=>6\(\sqrt{2}\)


Hope this helps !! :-D :-D


Thank you Abhishek, you made the math much more clear. However, I am still confused as to how the root 2 jumped to the top, and where the original 2 up top disappeared to.
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4689 [1]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   14 Apr 2016, 02:49
1
Kudos
bgbeidas wrote:
Thank you Abhishek, you made the math much more clear. However, I am still confused as to how the root 2 jumped to the top, and where the original 2 up top disappeared to.


I think you are referring to the the following part as under -

Quote:
\(\frac{2}{\sqrt{2}}\)


If that is the case then consider it this way -

\(\frac{2}{\sqrt{2}}\)

=>\((2 * \sqrt{2})/(\sqrt{2}* \sqrt{2})\)

=> \(2 * \sqrt{2}/2\)

=>\(\sqrt{2}\)

Hope this helps !! :-D :-D :-D
User avatar
D
stonecold
Alum
Joined: 12 Aug 2015
Posts: 2282
Own Kudos [?]: 3130 [1]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Send PM
GMAT ToolKit User
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   15 Apr 2016, 02:30
1
Kudos
bgbeidas wrote:
Abhishek009 wrote:
bgbeidas wrote:

=>\((\sqrt{2}*\sqrt[3]{3})^3\)
=> \(2\sqrt{2}*3 = 6\sqrt{2}\)
C

I understand how you got 3, and how you should gt 2\sqrt{2} at the bottom.
But the 2 in the top part, when I cube it I get 8, not sure where that disappears in your process.



I think u are clear with this part =>\((\sqrt{2}*\sqrt[3]{3})^3\)

=>\((\sqrt{2}*\sqrt[3]{3})^3\)

=> (\(2^{1/2}\) * \(3^{1/3}\))\(^{3}\)

=> \(2^{3/2}\)* \(3^{3/3}\)

=>\(2^1\)* \(2^{1/2}\)* \(3^1\) { Because \(\frac{3}{2}\) = \(1 \frac{1}{2}\) and \(\frac{3}{3}\) = 1 }

=> \(2^1\)* \(2^{1/2}\)* \(3^1\)

=> 2*\(\sqrt{2}\) * 3

=>6\(\sqrt{2}\)


Hope this helps !! :-D :-D


Thank you Abhishek, you made the math much more clear. However, I am still confused as to how the root 2 jumped to the top, and where the original 2 up top disappeared to.


ITS called " RATIONALISING THE DENOMINATOR"
avatar
Jaikuz
Intern
Intern
Joined: 05 Mar 2016
Posts: 8
Own Kudos [?]: 62 [0]
Given Kudos: 1
Send PM
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   14 May 2016, 15:17
Fantastic reply Abhishek009 and chetan2u, many thanks.

In my opinion, the key part here is writting everything as exponents and then resolving the ^3 equation.

Thanks once again
User avatar
mitko20m
Intern
Intern
Joined: 18 Jan 2012
Posts: 32
Own Kudos [?]: 332 [1]
Given Kudos: 37
Send PM
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   15 Jul 2016, 12:54
Abishek thank you! Super helpful. Could you clarify from the beginning how you got rid of the denominator listed in the question stem? It would be great if you could note why you did what you did next to the more complex lines.

Also, if you have any other lists of questions for roots, please share. Thanks!
User avatar
mitko20m
Intern
Intern
Joined: 18 Jan 2012
Posts: 32
Own Kudos [?]: 332 [3]
Given Kudos: 37
Send PM
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   16 Jul 2016, 07:49
3
Kudos
Never mind. I thought the original question was 2^3 instead of 3 root of 3...
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6275 [7]
Given Kudos: 1646
Send PM
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   03 Aug 2016, 09:53
4
Kudos
3
Bookmarks
Expert Reply
bgbeidas wrote:
Which of the following is equal to \((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)?

A) 3√2/2
B) 3√2
C) 6√2
D) 12
E) 12√2


We can simplify the expression inside the parentheses first.

Recall that x/√x = √x, so 2/√2 = √2 and hence 2 x (^3√3)/√2 = √2 x (^3√3)

Now we raise each term to the 3rd power:

[√2 x (^3√3)]^3 = (√2)^3 x (^3√3)^3 = 2√2 x 3 = 6√2

(Note: When we raise each factor to the 3rd power, we use the fact that:

(√x)^3 = x√x and (^3√x)^3 = x) .

Answer: C
avatar
jcava972
Intern
Intern
Joined: 27 Apr 2016
Posts: 3
Own Kudos [?]: 1 [1]
Given Kudos: 11
Send PM
GMAT ToolKit User
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   11 Aug 2016, 15:55
1
Kudos
Why does the original equation have to be simplified?

Why can't tip 6 from "Exponents and roots: Tips and hints" post by bunuel be applied in this situation? (Can't post links yet)

I understand that you can't, because if you distribute the exponent and raise all the individual elements to 3 you get 8*3 / 2sqrt2 and ultimately 12/sqrt2.

What rule am I violating?
User avatar
B
NealC
BSchool Moderator
Joined: 27 Feb 2014
Posts: 23
Own Kudos [?]: 16 [0]
Given Kudos: 5
Schools: Mason '21 Rotman '18 (WD)
Send PM
GMAT ToolKit User
GMAT PREP EXAM PACK 2 PROBLEM [#permalink] New post   15 Aug 2016, 05:36
Hi everyone,

Today I encounter this question on the one of the test on exam pack 2, and I cannot arrive at the OA of the question. Could anyone please help me solve it step by step?

Which of the following is equal to ( \(2^3\)\sqrt{\sqrt{3}}/2)\(3\)

A. \frac{3\sqrt{2}}{2}
B.3\sqrt{2}
C.6\sqrt{2}
D.12
E.12\sqrt{2}

Show Spoiler
OA is C
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619054 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   15 Aug 2016, 05:40
Expert Reply
NealC wrote:
Hi everyone,

Today I encounter this question on the one of the test on exam pack 2, and I cannot arrive at the OA of the question. Could anyone please help me solve it step by step?

Which of the following is equal to ( \(2^3\)\sqrt{\sqrt{3}}/2)\(3\)

A. \frac{3\sqrt{2}}{2}
B.3\sqrt{2}
C.6\sqrt{2}
D.12
E.12\sqrt{2}

Show Spoiler
OA is C


Merging topics.

Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html
User avatar
B
NealC
BSchool Moderator
Joined: 27 Feb 2014
Posts: 23
Own Kudos [?]: 16 [3]
Given Kudos: 5
Schools: Mason '21 Rotman '18 (WD)
Send PM
GMAT ToolKit User
Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   15 Aug 2016, 05:49
3
Kudos
AfricanPrincess wrote:
The way the question has been asked is ambiguous because of what looks like 2^3 in the numerator.

Posted from my mobile device


Totally agreed with you, I encountered this question today, and thought the number 3 in this case is the power of 2 and therefore can not arrived at the correct answer. I had to guess after 4m trying hopelessly to solve it, very frustrating as it is just the second question, I thought the answer is wrong. I think GMAT should make it clear which number belong to which.
User avatar
B
NealC
BSchool Moderator
Joined: 27 Feb 2014
Posts: 23
Own Kudos [?]: 16 [0]
Given Kudos: 5
Schools: Mason '21 Rotman '18 (WD)
Send PM
GMAT ToolKit User
Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   15 Aug 2016, 05:55
Bunuel wrote:
NealC wrote:
Hi everyone,

Today I encounter this question on the one of the test on exam pack 2, and I cannot arrive at the OA of the question. Could anyone please help me solve it step by step?

Which of the following is equal to ( \(2^3\)\sqrt{\sqrt{3}}/2)\(3\)

A. \frac{3\sqrt{2}}{2}
B.3\sqrt{2}
C.6\sqrt{2}
D.12
E.12\sqrt{2}

Show Spoiler
OA is C


Merging topics.

Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html


Sorry Bunuel,

I had tried to search it in the forum and cannot find the question. Therefore I though no one encounter it before and posted it. The way this question is worded made me very frustrated, I really want to look for its discussion, and thus when I couldn't find it, I immediately posted it. My apology, I will search harder the next time before attempting to post any question.
avatar
crowle35
Intern
Intern
Joined: 27 Mar 2016
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 58
Send PM
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink] New post   28 Aug 2016, 11:26
IMO - the wording on this problem is ambiguous. How am I supposed to know it is 2(CUBERT(3)) instead of 2^3(Sqrt(3))???
GMAT Club Bot
gmatclubot
Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]
28 Aug 2016, 11:26
 1   2   
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions