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THE ROOT OF THE ROOTS

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vicslick46
 Post subject: THE ROOT OF THE ROOTS
 Post Posted: Thu Nov 12, 2009 6:55 pm 
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Students


Posts: 1
Hi, this was the explanation given for the problem CAT problem (simplifying the equation), I see how cube root 80 turns into cube root 16*5, but how does it go from that, to 12*root 5?


√(█(∛ 80 + 3/(9+4√ 5) ((9-4√ 5))/(9-4√ 5))
=

√(█(∛(16*5)+(27-12√5)/(81-(16*5))
=

√(12√5+27-12√5)

=

√27
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helloriteshranjan
 Post subject: Re: THE ROOT OF THE ROOTS
 Post Posted: Fri Nov 13, 2009 4:12 pm 
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Students


Posts: 30
fishy step...!!
I mean wrong.

where does this problem appear?
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Ben Ku
 Post subject: Re: THE ROOT OF THE ROOTS
 Post Posted: Wed Jan 13, 2010 1:10 am 
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ManhattanGMAT Staff


Posts: 823
Quote:
Hi, this was the explanation given for the problem CAT problem (simplifying the equation), I see how cube root 80 turns into cube root 16*5, but how does it go from that, to 12*root 5?


3√ 80 is not the cube root of 80. instead it's 3 * √ 80.

3 * √ 80
= 3 * √ (16*5)
= 3 * 4 * √ 5
= 12 * √ 5

Hope that helps.

_________________
Ben Ku
Instructor
ManhattanGMAT
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sadat.sathak
 Post subject: Re: THE ROOT OF THE ROOTS
 Post Posted: Thu Oct 13, 2011 2:43 pm 
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Students


Posts: 4
The denominator of the second part under the root --> "81-(16)(5)" Seems to have dissapeared from the 2nd step onwards. What gives?
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jnelson0612
 Post subject: Re: THE ROOT OF THE ROOTS
 Post Posted: Sun Nov 20, 2011 12:30 am 
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ManhattanGMAT Staff


Posts: 1857
sadat.sathak wrote:
The denominator of the second part under the root --> "81-(16)(5)" Seems to have dissapeared from the 2nd step onwards. What gives?


When you solve that part out, you get 81 - 80 = 1, so the denominator of 1 can be safely removed from the equation. :-)

Best wishes,

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Jamie Nelson
ManhattanGMAT Instructor
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