Last visit was: 07 May 2026, 13:15 It is currently 07 May 2026, 13:15
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
655-705 (Hard)|   Roots|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 07 May 2026
Posts: 110,170
Own Kudos:
813,538
 [18]
Given Kudos: 106,102
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,170
Kudos: 813,538
 [18]
(2/(3a))^(1/3) 06 Jul 2017, 23:30
1
Kudos
Add Kudos
17
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

62% (01:44) correct 38% (01:49) wrong based on 532 sessions

History

Date
Time
Result
Not Attempted Yet
\(\sqrt[3]{\frac{2}{3a}}\)


A. \(\frac{\sqrt[3]{6a}}{3a}\)

B. \(\frac{\sqrt[3]{18a}}{3a}\)

C. \(\frac{\sqrt[3]{18a^2}}{3a}\)

D. 2

E. 6a
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
sashiim20
User avatar
Joined: 04 Dec 2015
Last visit: 05 Jun 2024
Posts: 608
Own Kudos:
1,980
 [5]
Given Kudos: 276
Location: India
Concentration: Technology, Strategy
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
Posts: 608
Kudos: 1,980
 [5]
(2/(3a))^(1/3) 07 Jul 2017, 05:59
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
\(\sqrt[3]{\frac{2}{3a}}\)


A. \(\frac{\sqrt[3]{6a}}{3a}\)

B. \(\frac{\sqrt[3]{18a}}{3a}\)

C. \(\frac{\sqrt[3]{18a^2}}{3a}\)

D. 2

E. 6a
Show more

Given the expression \(\sqrt[3]{\frac{2}{3a}}\)

Multiplying numerator and denominator with \((3a)^2\), we get;

\(\sqrt[3]{\frac{2*(3a)^2}{3a*(3a)^2}}\)

\(\sqrt[3]{\frac{2*9a^2}{(3a)^3}}\)

\(\frac{\sqrt[3]{18a^2}}{3a}\)

Answer (C)...
General Discussion
avatar
rahimk7
avatar
Joined: 06 May 2015
Last visit: 07 Oct 2019
Posts: 29
Own Kudos:
7
 [1]
Given Kudos: 1
Posts: 29
Kudos: 7
 [1]
(2/(3a))^(1/3) 06 Jul 2017, 23:54
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Substitute A=2 in Question stem

Then select the answer which gives same value for a=2

Posted from my mobile device
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,800
Own Kudos:
6,244
 [3]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,800
Kudos: 6,244
 [3]
(2/(3a))^(1/3) 07 Jul 2017, 00:04
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
We are given the expression \(\sqrt[3]{\frac{2}{3a}}\)

Multiplying and dividing by \((3a)^2\)

we will get \(\frac{\sqrt[3]{18a^2}}{\sqrt[3]{27a^3}}\) = \(\frac{\sqrt[3]{18a^2}}{\sqrt[3]{(3a)^3}}\) = \(\frac{\sqrt[3]{18a^2}}{3a}\)(Option C)
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,732
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,732
(2/(3a))^(1/3) 12 Jul 2017, 16:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
\(\sqrt[3]{\frac{2}{3a}}\)


A. \(\frac{\sqrt[3]{6a}}{3a}\)

B. \(\frac{\sqrt[3]{18a}}{3a}\)

C. \(\frac{\sqrt[3]{18a^2}}{3a}\)

D. 2

E. 6a
Show more

In order to rationalize the denominator of this cube root problem, we must have a perfect cube in the denominator of the fraction. Thus, we have to multiply the numerator and denominator by the square of the denominator:

3^√(2/3a) * 3^√(9a^2/9a^2)

3^√(18a^2/27a^3)

3^√(18a^2)/3^√(27a^3)

3^√(18a^2)/3a

Answer: C
User avatar
omavsp
User avatar
Joined: 20 Aug 2017
Last visit: 28 Jan 2024
Posts: 34
Own Kudos:
15
Given Kudos: 191
Products:
My Reviews
Posts: 34
Kudos: 15
(2/(3a))^(1/3) 02 Jul 2019, 08:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
\(\sqrt[3]{\frac{2}{3a}}\)


A. \(\frac{\sqrt[3]{6a}}{3a}\)

B. \(\frac{\sqrt[3]{18a}}{3a}\)

C. \(\frac{\sqrt[3]{18a^2}}{3a}\)

D. 2

E. 6a
Show more


Dear Bunuel,

can you please explain how people here came up with Multiplying and dividing by \((3a)^2\).

Im having hard time with reaching the right numbers in such circumstances.

Thank you so much!
avatar
menonrit
avatar
Joined: 07 May 2018
Last visit: 07 Jul 2019
Posts: 33
Own Kudos:
8
Given Kudos: 12
Posts: 33
Kudos: 8
(2/(3a))^(1/3) 05 Jul 2019, 13:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JeffTargetTestPrep
Bunuel
\(\sqrt[3]{\frac{2}{3a}}\)


A. \(\frac{\sqrt[3]{6a}}{3a}\)

B. \(\frac{\sqrt[3]{18a}}{3a}\)

C. \(\frac{\sqrt[3]{18a^2}}{3a}\)

D. 2

E. 6a

In order to rationalize the denominator of this cube root problem, we must have a perfect cube in the denominator of the fraction. Thus, we have to multiply the numerator and denominator by the square of the denominator:

3^√(2/3a) * 3^√(9a^2/9a^2)

3^√(18a^2/27a^3)

3^√(18a^2)/3^√(27a^3)

3^√(18a^2)/3a

Answer: C
Show more

Hi why can't we not raise this function to the power of 3: ((2/3a)^1/3)^3

Leaving our answer as 2.
avatar
georgethomps
avatar
Joined: 07 Mar 2019
Last visit: 28 Jul 2025
Posts: 21
Own Kudos:
14
 [2]
Given Kudos: 2
Posts: 21
Kudos: 14
 [2]
(2/(3a))^(1/3) 05 Jul 2019, 14:54
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
omavsp
Bunuel
\(\sqrt[3]{\frac{2}{3a}}\)


A. \(\frac{\sqrt[3]{6a}}{3a}\)

B. \(\frac{\sqrt[3]{18a}}{3a}\)

C. \(\frac{\sqrt[3]{18a^2}}{3a}\)

D. 2

E. 6a


Dear Bunuel,

can you please explain how people here came up with Multiplying and dividing by \((3a)^2\).

Im having hard time with reaching the right numbers in such circumstances.

Thank you so much!
Show more
Saying you multiply the numerator and denominator by (3a)^2 is a poor explanation, they meant to say to multiply it by ((3a)^2)^1/3.

Taking the cubed root is the equivalent of raising x^1/3. Thus, to make the denominator 3a, we need to multiply it by (3a)^2/3, since 1/3 + 2/3 = 1, in which case it would be (3a)^1.

Posted from my mobile device
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,679
Own Kudos:
1,472
Given Kudos: 607
Location: United States
Posts: 1,679
Kudos: 1,472
(2/(3a))^(1/3) 14 Aug 2019, 04:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
\(\sqrt[3]{\frac{2}{3a}}\)

A. \(\frac{\sqrt[3]{6a}}{3a}\)
B. \(\frac{\sqrt[3]{18a}}{3a}\)
C. \(\frac{\sqrt[3]{18a^2}}{3a}\)
D. 2
E. 6a
Show more

rationalize the denominator:
\(\sqrt[3]{\frac{2}{3a}}•\sqrt[3]{\frac{(3a)^2}{(3a)^2}}=\frac{\sqrt[3]{2(3a)^2}}{3a}=\frac{\sqrt[3]{18a^2}}{3a}\)

Answer (C).
User avatar
shahsahil2101
User avatar
Joined: 20 Feb 2025
Last visit: 07 May 2026
Posts: 17
Given Kudos: 4
Location: India
Concentration: Strategy, Entrepreneurship
GMAT Focus 1: 635 Q87 V78 DI79
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 1: 635 Q87 V78 DI79
Posts: 17
Kudos: 0
(2/(3a))^(1/3) 03 May 2026, 06:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
One of the other ways is to substitute a value, assume a=2 and substitute in all options
Moderators:
Bunuel
Math Expert
110170 posts
Krunaal
Tuck School Moderator
852 posts