If n = (-72)^(1/3) then the value of n is

Let m= (-72)^1/3
Hence m^3 = -72

Lets check

-1^3 => -1
-2^3 => -8
-3^3 => -27
-4^3 => -64
-5^3 => -125

Hence m must be between (-5,-4)
Hence E.

\(n = (-72)^{(\frac{1}{3})}\)

Cubing both sides, we get;

\(n^3 = (-72)\)

\(-4^3 = -64\)

\(-5^3 = -125\)

Therefore value of n has to be between, -5 and -4.

\(-5 < n < -4\). Answer (E) ...

Since \(n = (-72)^{(\frac{1}{3})}\) ,n is definitely negative.

72, when prime-factorized will give \(2^3 * 3^2\)
Cube root of \(2^3\)(8)is 2
Cube root of \(3^2\)(9) is a little more than 2

Hence \((-72)^{(\frac{1}{3})}\) is a little more than -4
This comes in the range -5 < n < -4(Option E)

IMO, E.

Rewritten the question becomes what is the cube root of 72?

4^3 = 64, so N is greater than 4

5^3 = 125, so N is less than 5

E) N is between -4 and -5

Hi All,

While you will almost certainly have to deal with a square-root a couple of times on Test Day (in both Arithmetic and Geometry questions), cube-roots are relatively rare (you probably won't see them at all on Test Day). That having been said, cube-roots are based on the same general math concepts as square-roots.

For example...
The square-root of 4 is +2 ... since (2)(2) = 4
The cube-root of 27 is +3 ... since (3)(3)(3) = 27
The cube-root of -27 is -3 ... since (-3)(-3)(-3) = -27

In this question, we're asked for the cube-root of -72, but the solution will NOT be an integer (notice how the answer choices are all RANGES - that's a hint that N is not an integer AND that we don't actually have to find the exact value of N; we just have to figure out what numbers it is between). Thus, we have to look for cubes of negative integers:

(-3)^3 = -27
(-4)^3 = -64
(-5)^3 = -125

Since -72 is between -64 and -125, the cube-root of -72 has to be between -4 and -5

Final Answer:

GMAT assassins aren't born, they're made,
Rich

We need to find two integers, one of which,, when raised to the 3rd power, is less than -72, and the other of which, when raised to the 3rd power, is greater than -72.

Since -4^3 = -64 and -5^3 = -125, and since -72 is between those two numbers, n must be between -4 and -5.

Answer: E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.