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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
Joined: 28 Dec 2011
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If cube root of square root of x equals x/5, then x could eq  [#permalink]

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24 Jul 2014, 16:22
3
14
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:42) correct 35% (01:53) wrong based on 319 sessions

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Attachment:

cube root of square root.JPG [ 15.32 KiB | Viewed 4167 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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Mike McGarry
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If cube root of square root of x equals x/5, then x could eq  [#permalink]

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Updated on: 10 Mar 2015, 05:08
12
2

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

$$x = 5 * x^{\frac{1}{6}}$$

$$x^{1-\frac{1}{6}} = 5$$

$$x^{\frac{5}{6}} = 5$$

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.
Edited.
##### General Discussion
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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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10 Mar 2015, 03:13
But answer D is 5$$\sqrt{5^6}$$
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Joined: 02 Sep 2009
Posts: 58443
Re: If cube root of square root of x equals x/5, then x could eq  [#permalink]

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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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15 Apr 2016, 02:53
PareshGmat wrote:

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

$$x = 5 * x^{\frac{1}{6}}$$

$$x^{1-\frac{1}{6}} = 5$$

$$x^{\frac{5}{6}} = 5$$

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

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