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The Value of Cube Root of -89 is

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mukund.jagadish
 Post subject: The Value of Cube Root of -89 is
 Post Posted: Fri Jan 22, 2010 4:10 pm 
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Source: GMAT Prep Test #2

The Value of Cube Root -89 is:
a. between -9 and -10
b. between -8 and -9
c. between -4 and -5
d. between -3 and -4
e. undefined

Could someone please walk me through this. In high school I learned that negative square roots are imaginary numbers. For example the square of -4 would be 2i. This reasoning led me to choose answer E, but it is incorrect.
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zchampz
 Post subject: Re: The Value of Cube Root of -89 is
 Post Posted: Fri Jan 22, 2010 4:18 pm 
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Answer is C

It is between -4 and -5.

One way to look is: cube of -4 is -64 and cube of -5 is -125. As -125<-89<-64, the cube root of -89 will be between -4 and -5.

Hope it helps.
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mukund.jagadish
 Post subject: Re: The Value of Cube Root of -89 is
 Post Posted: Fri Jan 22, 2010 4:22 pm 
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Thanks zchampz, that makes perfect sense.
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RonPurewal
 Post subject: Re: The Value of Cube Root of -89 is
 Post Posted: Thu Mar 04, 2010 10:24 am 
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ManhattanGMAT Staff


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zchampz wrote:
Answer is C

It is between -4 and -5.

One way to look is: cube of -4 is -64 and cube of -5 is -125. As -125<-89<-64, the cube root of -89 will be between -4 and -5.

Hope it helps.


yep.

if you want more practice on this sort of thing, you can search the internet for the term "interpolation".
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jp.jprasanna
 Post subject: Re: The Value of Cube Root of -89 is
 Post Posted: Thu Mar 15, 2012 4:14 pm 
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OK even I had the same doubt so In GMAT only square root any - ve nos is imaginary correct? ex x^2 = -9 = no solution

But x^3 = -27 = 3.. Correct?

Cheers
Jp
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jnelson0612
 Post subject: Re: The Value of Cube Root of -89 is
 Post Posted: Sat Mar 17, 2012 11:30 pm 
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ManhattanGMAT Staff


Posts: 1857
jp.jprasanna wrote:
OK even I had the same doubt so In GMAT only square root any - ve nos is imaginary correct? ex x^2 = -9 = no solution

But x^3 = -27 = 3.. Correct?

Cheers
Jp


Exactly! You've got it. :-)

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Jamie Nelson
ManhattanGMAT Instructor
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