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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).

The even root from negative power is undefined, for GMAT. For example: (negative number)^{1/2k} is undefined, (-8)^1/2 or (-3.5)^1/8 or (-1)^1/22. But the odd root can be found.

(-2)*(-2)*(-2)=-8 so (-8)^1/3=-2 or (-4)*(-4)*(-4)=-64 so (-64)^1/3=-4.

The question you posted is quite tricky:

(-89)^1/3 is more than -5 (-5^3=-125) but less than -4 (-4^3=-64) --> -5<x<-4, (actually it's ~-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.

forgot to answer the question...just curious if you typed the answers correctly...

i thought this was pretty simple by taking the answer options. E was out of question as the Bunual rightly mentioned.

only by looking at the lower limits of the ranges, we can discard option C and D.

Option B was a short ranged between -8 to -9 and the squares of these numbers are near 89. cube must be very high. without actually solving it, we can ignore it. Remaining option has to be the right one i.e. A.

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.

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?
_________________

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.

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.
_________________

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

My guess (D) was incorrect because I guess I did \(\sqrt[4]{-81}= -3\) and \(\sqrt[3]{-64}= -4\)

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.
_________________

Re: The value of cube root of (-89) is: [#permalink]

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06 Jun 2013, 06:58

tejal777 wrote:

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

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

Very tricky question.

Questions seeks to find out for a range of numbers that include a number after multiplying it by itself gives -89. First thing we know is that it is a negative number. We can easily check few numbers, take -3*-3*-3=-27 too low, -4*-4*-4=-64 still low, -5*-5*-5=-125 too big. So basically it should be a number between -4 and -5. Do we have such range? Trick here is that it is tmpting automatically go to choice C. But this is wrong choice because it does not cover the range required. The only range that includes number between -4 and -5 is A. Although it is very broad and covers many other values, but we have never been restricted. So the choice the A is the best!
_________________

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