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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

If \(n = (-72)^{(\frac{1}{3})}\) then the value of n is

A. -9 < n < -8 B. -8 < n < -7 C. -7 < n < -6 D. -6 < n < -5 E. -5 < n < -4

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
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