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The value of (-89)^(1/3) is:

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Bunuel
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The value of (-89)^(1/3) is: [#permalink] New post   08 Oct 2018, 03:15
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The value of \(\sqrt[3]{-89}\) is:

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

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Bunuel
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Re: The value of (-89)^(1/3) is: [#permalink] New post   04 Mar 2019, 21:42
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jfranciscocuencag wrote:
Why is it C?

Shouldn't be undifined?


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 \(\sqrt[3]{-64} =-4\).
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Re: The value of (-89)^(1/3) is: [#permalink] New post   08 Oct 2018, 08:53
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Bunuel wrote:
The value of \(\sqrt[3]{-89}\) is:

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


\(-5^3 < 89 < -4^3\)

Or, \(-125< - 89 < -64\), Hence, Answer must be (C)
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Re: The value of (-89)^(1/3) is: [#permalink] New post   13 Jun 2022, 11:53
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Bunuel wrote:
The value of \(\sqrt[3]{-89}\) is:

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



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
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Re: The value of (-89)^(1/3) is: [#permalink] New post   04 Mar 2019, 18:01
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Why is it C?

Shouldn't be undifined?
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Re: The value of (-89)^(1/3) is: [#permalink] New post   07 Mar 2019, 07:55
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Bunuel wrote:
The value of \(\sqrt[3]{-89}\) is:

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


Since (-4)^3 = -64 and (-5)^3 = -125, the 3rd root of -89 is between -4 and -5.

Answer: C
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Bunuel
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Re: The value of (-89)^(1/3) is: [#permalink] New post   08 Oct 2018, 03:19
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Bunuel wrote:
The value of \(\sqrt[3]{-89}\) is:

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


The same question with different options: https://gmatclub.com/forum/the-value-of ... 86290.html
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Re: The value of (-89)^(1/3) is: [#permalink] New post   05 Mar 2019, 08:21
Bunuel wrote:
The value of \(\sqrt[3]{-89}\) is:

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



3√-5= -125 and 3√-4 = -64
value -89 will lie in between them
IMO C
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Re: The value of (-89)^(1/3) is: [#permalink] New post   16 Oct 2023, 03:21
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Re: The value of (-89)^(1/3) is: [#permalink]
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