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If cube root of square root of x equals x/5, then x could eq

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Magoosh GMAT Instructor
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If cube root of square root of x equals x/5, then x could eq  [#permalink]

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New post 24 Jul 2014, 16:22
3
10
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:41) correct 35% (01:54) wrong based on 285 sessions

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cube root of square root.JPG
cube root of square root.JPG [ 15.32 KiB | Viewed 3810 times ]


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

Mike :-)
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If cube root of square root of x equals x/5, then x could eq  [#permalink]

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New post Updated on: 10 Mar 2015, 05:08
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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 \(\frac{6}{5}\)

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

\(x = \sqrt[5]{5^6}\)
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Originally posted by PareshGmat on 24 Jul 2014, 20:08.
Last edited by Bunuel on 10 Mar 2015, 05:08, edited 1 time in total.
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Re: If cube root of square root of x equals x/5, then x could eq  [#permalink]

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New post 10 Mar 2015, 03:13
But answer D is 5\(\sqrt{5^6}\)
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Re: If cube root of square root of x equals x/5, then x could eq  [#permalink]

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New post 10 Mar 2015, 05:08
erikvm wrote:
But answer D is 5\(\sqrt{5^6}\)


There was a formatting error. The solution is correct.

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

\(x = \sqrt[5]{5^6}\)
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Re: If cube root of square root of x equals x/5, then x could eq  [#permalink]

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New post 15 Apr 2016, 02:53
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..
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Re: If cube root of square root of x equals x/5, then x could eq  [#permalink]

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New post 17 Feb 2019, 11:26
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:
http://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
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Re: If cube root of square root of x equals x/5, then x could eq   [#permalink] 17 Feb 2019, 11:26
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