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If x^(1/6) = 6, then √x^6 is ?

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carcass
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If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   Updated on: 31 Mar 2012, 01:22
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If x^(1/6) = 6, then √x^6 is ?

A. 6
B. 6√6
C. 6^6
D. 6^18
E. 6^36
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Official Answer
D

Originally posted by carcass on 30 Mar 2012, 18:17.
Last edited by Bunuel on 31 Mar 2012, 01:22, edited 1 time in total.
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Bunuel
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   31 Mar 2012, 01:21
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If \(\sqrt[6]{x}= 6\), then \(\sqrt{x^6}\) is ?
A. 6
B. 6√6
C. 6^6
D. 6^18
E. 6^36

\(\sqrt[6]{x}= 6\) --> \(x=6^6\). So, \(\sqrt{x^6}=x^3=(6^6)^3=6^{18}\).

Answer: D.
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carcass
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   31 Mar 2012, 03:11
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Thanks , however.

Sometimes I'm intimidated from the question.

For the second part was clear: x^6/3 = x^3 and then substitution.

The first part was so simple.....likewise. :(

Thanks
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   01 Apr 2012, 07:11
bunnel

how did you come x=6^6,please explain
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   Updated on: 01 Apr 2012, 09:23
TomB wrote:
bunnel

how did you come x=6^6,please explain

because to cancel out your root you have to raise the same to the exponent of the same and at the same time raise the other part of the equation.

For instance: if you have √x= 4 rise to power of 2 both side; so you'll have x=16 or 3√x=4 then you'll have x=64 (rise to power of 3).

So we have x=6^6; of course in our case we do not need to obtain 6^6 (46656). we care about to substitute this value to our x and then resolve our problem. It was simple but me too was confused looking at the problem.

I ask to Bunuel to correct me if I'm wrong.

Originally posted by carcass on 01 Apr 2012, 07:20.
Last edited by carcass on 01 Apr 2012, 09:23, edited 1 time in total.
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   01 Apr 2012, 08:38
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TomB wrote:
bunnel

how did you come x=6^6,please explain


\(\sqrt[6]{x}= 6\) --> raise to the sixth power: \((\sqrt[6]{x})^6= 6^6\) --> \(x=6^6\).

Hope it's clear.
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   01 Apr 2012, 16:35
Vote for D

this is one to bookmark

x^1/6 = 6

raise the power to 6

x^6/6 = 6^6

therefore

x = 6^6

now

=x^6/2
=x^3
=(6^6)^3
=6^18
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   29 Apr 2012, 11:15
carcass wrote:
If x^(1/6) = 6, then √x^6 is ?

A. 6
B. 6√6
C. 6^6
D. 6^18
E. 6^36




Ans explanation

x^(1/6) can be written as 6\sqrt{x}

so 6\sqrt{x}=6

by raising to the power of six both sides we get

(6\sqrt{x})^6=6^6

we get x=6^6

\sqrt{x} ^6=(\sqrt{6^6})

(6^6/2)6=(6^3)^6=6^3*6=6^18
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   05 Jun 2013, 04:28
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   05 Jun 2013, 07:39
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\(\sqrt{x}^6\) can be rewritten as \(x^3\)
if \(\sqrt[6]{x} = 6\) and \((\sqrt[6]{x})^1^8 = x^3\), then \(x^3 = 6^1^8\)
Answer is D
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   06 Jun 2013, 07:20
In such cases i always try to find some simple number for which i am sure and make simple but similar calculation.
For example in our case we have x^(1/6)=6 from a glance it is difficult to get what is this number, but if we take \(\sqrt{x}\)=2 we see that x is 4, because x^1/2=2 is the same as to say 2 multiplied by itself once. In our case we have x^(1/6)=6 using our logic that means x=6^6.
In the second expression we have (x^6)^1/2 ---> (x)^6*1/2=x^3

Now the easiest part, since we know that x=6^6 then x^3=(6^6)^3=6^18

Answer choice D.
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   26 Feb 2014, 23:29
x^1/6 = 6
We require to find x^3
So power both sides by 18

Answer = 6^18 = D
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   08 Mar 2014, 10:28
Option D.
X^1/6=6
Therefore x=6^6
We're asked x^3
Cubing both sides above
We get x^3=6^18

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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post   20 Mar 2018, 16:54
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carcass wrote:
If x^(1/6) = 6, then √x^6 is ?

A. 6
B. 6√6
C. 6^6
D. 6^18
E. 6^36


Simplifying the equation, we have:

x^(1/6) = 6

x = 6^6

So √x^6 = √(6^6)^6 = √6^36 = 6^18

Answer: D
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Re: If x^(1/6) = 6, then x^6 is ? [#permalink] New post   30 Jun 2022, 08:45
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