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If x^(1/6) = 6, then √x^6 is ?

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If x^(1/6) = 6, then √x^6 is ? [#permalink] New post 30 Mar 2012, 17:17
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64% (01:45) correct 36% (00:46) wrong based on 245 sessions

Last edited by Bunuel on 31 Mar 2012, 00:22, edited 1 time in total.
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post 31 Mar 2012, 00:21
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post 31 Mar 2012, 02:11
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post 01 Apr 2012, 06:11
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 01 Apr 2012, 06:20
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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.
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Last edited by carcass on 01 Apr 2012, 08:23, 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, 07:38
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post 01 Apr 2012, 15:35
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, 10:15
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, 03:28
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Re: If x^(1/6) = 6, then √x^6 is ? [#permalink] New post 05 Jun 2013, 06:39
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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, 06:20
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, 22:29
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, 09:28
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] 08 Mar 2014, 09:28
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