The value of cube root of (-89) is:

Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): \(\sqrt[{even}]{negative}=undefined\), for example \(\sqrt{-25}=undefined\).

Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

The above question is quite tricky:

\(\sqrt[3]{-89}\) is more than -5 (as \(-5^3=-125\)) but less than -4 (as \(-4^3=-64\)) --> \(-5<x<-4\), (actually it's \(\approx{-4.5}\)). So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10).

Answer: A.
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Hey bunuel

i did this quesiton wrong cuz remember your words that \(\sqrt{-25}=undefined\).

cube root means that it has to be a negative number after you took out. Then it should be something \sqrt{negative X} therefore should be undefined? where am i missing?

Not sure that understand your question. But again:

Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): \(\sqrt[{even}]{negative}=undefined\), for example \(\sqrt{-25}=undefined\).

Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

Or:
\(\sqrt[{even}]{positive}=positive\): \(\sqrt{25}=5\). Even roots have only a non-negative value on the GMAT.

\(\sqrt[{even}]{negative}=undefined\): \(\sqrt{-25}=undefined\). Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers).

\(\sqrt[{odd}]{positive}=positive\) and \(\sqrt[{odd}]{negative}=negative\): \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\). Odd roots will have the same sign as the base of the root.
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Are these 2 different questions ? Bunnels post says merging similar topics and they have different OA's ...I am not sure what the difference is ?

The value of cube root of (-89) is..?

Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined


AND



\(\sqrt[3]{-89}\) is:

A) Between -9 and -10
B) Between -8 and -9
C) Between -4 and -5
D) Between -3 and -4
E) Undefined

The questions are the same but as Bunuel mentioned while merging, the answer options are different "Between -4 and 5" and "Between -4 and -5"
The answer lies between -4 and -5 but not between -4 and 5 so the range which covers '-4 to -5' is '-9 to 10' in the first question.
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Hi! Can you explain this: So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10). ? I don't understand it. Thank you.

The question asks about the range the cube root of (-89) is. We found that it's between -5 and -4, approximately -4.5. Now, can you tell me in which range from the options given is -4.5?
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BTW, i noticed that the range given in option A -9 to +10, is the widest of all and covers all other ranges in the options. So, whatever falls in other ranges, will fall in this range. And this is an official question.
So, on the real test, why cant i just mark option A blindly and move on?

also, since no two options can be correct, option A has to win.

Yes, if it is defined, it will certainly lie in the range -9 and 10 since it covers all other ranges. So answer would be (A).
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Main idea: The cube root should be within the range even though the range may be large

Details: Cube root of -89 is between -4 and -5.

This is only in the range given in choice A .
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Such a poser!

You intuitively look for the option -4 to -5, but of course the options are messed up.

Important: Recognize that \(-89\) is between \(-64\) and \(-125\)
In other words: \(-125 < -89 < -64\)

Since \((-5)^3 = -125\), we know that \(\sqrt[3]{-125} = -5\)
Since \((-4)^3 = -64\), we know that \(\sqrt[3]{-64} = -4\)

Since \(-89\) is between \(-64\) and \(-125\), we know that \(\sqrt[3]{-89}\) will be between \(\sqrt[3]{-64}\) and \(\sqrt[3]{-125}\)
In other words, \(\sqrt[3]{-89}\) will be between \(-4\) and \(-5\)

Answer: C

That is actually pretty smart. You would still need to confirm first that the cube root is actually defined - so you could eliminate E.

But yes, after rejecting answer choice E, once you understand that the range mentioned in A anyway is a superset of the other ranges, you could confidently select A as your answer.