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