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# which of the following CANNOT be the value of sqrt(288kx)

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Manager
Joined: 02 Aug 2007
Posts: 221
Schools: Life
which of the following CANNOT be the value of sqrt(288kx) [#permalink]

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12 Jan 2009, 19:59
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If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of sqrt(288kx)?
A. 24k*sqrt(3)
B. 24*sqrt(k)
C. 24*sqrt(3k)
D. 24*sqrt(6k)
E. 72*sqrt(k)
SVP
Joined: 29 Aug 2007
Posts: 2453
Re: which of the following CANNOT be the value of sqrt(288kx) [#permalink]

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12 Jan 2009, 20:19
x-ALI-x wrote:
If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of sqrt(288kx)?

A. 24k*sqrt(3)
B. 24*sqrt(k)
C. 24*sqrt(3k)
D. 24*sqrt(6k)
E. 72*sqrt(k)

= sqrt(288kx)
= sqrt{(2x2x2x2x2x3x3)(k)(x)}
= sqrt{(2^5 x 3^2)(k)(6i)}
= sqrt{(2^6 x 3^3)(ki)}
= (2^3 x 3) sqrt(3ki)
= 24 sqrt(3ki)

A. 24k*sqrt(3) ------ possible if k=i=1.
B. 24*sqrt(k) ------ possible only if i = 1/3 but i annot be 1/3. If i is 1/3, x has to be 2, which is not a multiple of 6. so B is not possible.
C. 24*sqrt(3k) ------ possible if i=1.
D. 24*sqrt(6k) ------ possible i=2 or x = 12
E. 72*sqrt(k) ------ possible if i=3 or x = 18

so B.
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Re: which of the following CANNOT be the value of sqrt(288kx)   [#permalink] 12 Jan 2009, 20:19
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# which of the following CANNOT be the value of sqrt(288kx)

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