Last visit was: 23 May 2024, 05:30 It is currently 23 May 2024, 05:30
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4461
Own Kudos [?]: 28670 [35]
Given Kudos: 130
Most Helpful Reply
avatar
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1559
Own Kudos [?]: 7238 [18]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
General Discussion
User avatar
Manager
Manager
Joined: 26 Feb 2015
Posts: 94
Own Kudos [?]: 204 [0]
Given Kudos: 43
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 93417
Own Kudos [?]: 626023 [0]
Given Kudos: 81940
Send PM
Re: If cube root of square root of x equals x/5, then x could eq [#permalink]
Expert Reply
erikvm wrote:
But answer D is 5\(\sqrt{5^6}\)


There was a formatting error. The solution is correct.

\(x = 5^{\frac{6}{5}}\)

\(x = \sqrt[5]{5^6}\)
Alum
Joined: 12 Aug 2015
Posts: 2279
Own Kudos [?]: 3166 [0]
Given Kudos: 893
GRE 1: Q169 V154
Send PM
Re: If cube root of square root of x equals x/5, then x could eq [#permalink]
PareshGmat wrote:
Answer = D

\({(x^{\frac{1}{2}})}^{\frac{1}{3}} = \frac{x}{5}\)

\(x = 5 * x^{\frac{1}{6}}\)

\(x^{1-\frac{1}{6}} = 5\)

\(x^{\frac{5}{6}} = 5\)

Powering both sides by \(\frac{6}{5}\)

\(x = 5^{\frac{6}{5}}\)

\(x = \sqrt[5]{5^6}\)


Although not mentioned int the options
X may be zero too..
Director
Director
Joined: 04 Sep 2015
Posts: 552
Own Kudos [?]: 437 [0]
Given Kudos: 123
Location: India
WE:Information Technology (Computer Software)
Send PM
Re: If cube root of square root of x equals x/5, then x could eq [#permalink]
mikemcgarry wrote:
Attachment:
cube root of square root.JPG


For the OE to this question, as well as a bank of other challenging problems on Powers & Roots, see:
https://magoosh.com/gmat/2014/practice-p ... and-roots/

Mike :-)



given : (x^1/2)^1/3=x/5

then its also equal to 5*(x^1/2)^1/3=x,


then 5* (x^1/6)=x


then raising both sides by power 6 we get


5^6*x=x^6 or 5^6=x^5 or 5^6 root 5
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33152
Own Kudos [?]: 829 [0]
Given Kudos: 0
Send PM
Re: If cube root of square root of x equals x/5, then x could eq [#permalink]
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.
GMAT Club Bot
Re: If cube root of square root of x equals x/5, then x could eq [#permalink]
Moderator:
Math Expert
93417 posts