The Value of Cube Root of -89 is

[mukund.jagadish]

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.

[zchampz]

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.

[mukund.jagadish]

Thanks zchampz, that makes perfect sense.

[RonPurewal]

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".

[jp.jprasanna]

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

[jnelson0612]

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. :-)