Last visit was: 19 Jul 2025, 20:51 It is currently 19 Jul 2025, 20:51
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
Sub 505 Level|   Roots|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
742,809
 [14]
Given Kudos: 98,235
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: 102,627
Kudos: 742,809
 [14]
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] 10 May 2017, 11:57
2
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

84% (01:40) correct 16% (02:13) wrong based on 428 sessions

History

Date
Time
Result
Not Attempted Yet
What is the value of \((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\)?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8
ShowHide Answer
Official Answer
D
avatar
nishantt7
avatar
Joined: 05 May 2016
Last visit: 09 Feb 2021
Posts: 42
Own Kudos:
22
 [2]
Given Kudos: 150
Status:Preparing
Location: India
Concentration: International Business, Finance
Posts: 42
Kudos: 22
 [2]
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] 10 May 2017, 12:53
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
What is the value of \((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\)?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

Expression will become 512^(2*1/3*1/2*1/3)

So we are left with (512)^(1/3*1/3)

cube root of 512 is 8. So we are now left with 8^1/3 which is 2.

Answer is option D.
User avatar
sashiim20
User avatar
Joined: 04 Dec 2015
Last visit: 05 Jun 2024
Posts: 612
Own Kudos:
1,809
 [1]
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: 612
Kudos: 1,809
 [1]
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] 11 May 2017, 03:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel wrote:
What is the value of \((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\)?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

\((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\) -------(cube root of 512 = 8)
= \((\sqrt[3]{\sqrt8})^2\) ------- (squaring \((\sqrt{8})^2\) we get 8 )
= \((\sqrt[3]{8})\)
= \((\sqrt[3]{8})\) = 2
Answer D...

_________________
Kindly press "+1 Kudos" to appreciate :)
User avatar
mohshu
User avatar
Joined: 21 Mar 2016
Last visit: 26 Dec 2019
Posts: 426
Own Kudos:
133
Given Kudos: 103
Products:
My Reviews
Posts: 426
Kudos: 133
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] 11 May 2017, 04:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
512 = 8*8*8..

hence solving the expression gives as 2

ans D
User avatar
broall
User avatar
Retired Moderator
Joined: 10 Oct 2016
Last visit: 07 Apr 2021
Posts: 1,138
Own Kudos:
6,956
 [1]
Given Kudos: 65
Status:Long way to go!
Location: Viet Nam
Posts: 1,138
Kudos: 6,956
 [1]
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] 11 May 2017, 09:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the value of \((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\)?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

\(\Bigg (\sqrt[3]{\sqrt{\sqrt[3]{512}}}\Bigg )^2=\bigg (\sqrt[3]{\sqrt{8}} \bigg )^2 \\
= \bigg (\sqrt[3]{\sqrt{2^3}} \bigg )^2=\big (\sqrt{2} \big )^2=2\)

Or we could solve in this way:

\(\Bigg (\sqrt[3]{\sqrt{\sqrt[3]{512}}}\Bigg )^2 =\Bigg (\sqrt[3]{\sqrt{512^{\frac{1}{3}}}}\Bigg )^2 \\
= \Bigg (\sqrt[3]{\Big ( 512^{\frac{1}{3}} \Big )^{\frac{1}{2}}}\Bigg )^2 = \Bigg (\sqrt[3]{ 512^{\frac{1}{6}} }\Bigg )^2 \\
= \Bigg ( \Big (512^{\frac{1}{6}} \Big ) ^ {\frac{1}{3}}\Bigg )^2 = \Bigg ( 512^{\frac{1}{18}}\Bigg )^2 \\
= 512^{\frac{1}{9}} = (2^9)^{\frac{1}{9}} = 2\)
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Jul 2025
Posts: 16,115
Own Kudos:
74,410
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,115
Kudos: 74,410
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] 11 May 2017, 09:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the value of \((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\)?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

Every cube root can be replaced by 1/3 and square root can be replaced by 1/2 in the power.

\(512 = 2^9\)

\((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\)

\(= (2^9)^{2*(1/3)*(1/2)*(1/3)}\)

\(= 2\)
User avatar
shashankism
User avatar
Joined: 13 Mar 2017
Last visit: 23 Dec 2024
Posts: 611
Own Kudos:
671
Given Kudos: 88
Affiliations: IIT Dhanbad
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy)
Posts: 611
Kudos: 671
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] 12 May 2017, 04:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the value of \((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\)?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

\((\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2\)
= (512)^(2*1/3*1/2*1/3)
= (512)^1/9
= 2

Show Spoiler
Answer D.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,453
Own Kudos:
1,013
Posts: 37,453
Kudos: 1,013
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] 12 Feb 2025, 04:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
102627 posts
Krunaal
PS Forum Moderator
698 posts