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

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Math Expert
Joined: 02 Sep 2009
Posts: 61396
The value of (-89)^(1/3) is:  [#permalink]

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08 Oct 2018, 02:15
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15% (low)

Question Stats:

70% (00:50) correct 30% (00:50) wrong based on 228 sessions

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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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Re: The value of (-89)^(1/3) is:  [#permalink]

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07 Mar 2019, 06:55
1
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.

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Math Expert
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Re: The value of (-89)^(1/3) is:  [#permalink]

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08 Oct 2018, 02:19
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]

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08 Oct 2018, 07:53
1
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]

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04 Mar 2019, 17:01
Why is it C?

Shouldn't be undifined?
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Joined: 02 Sep 2009
Posts: 61396
Re: The value of (-89)^(1/3) is:  [#permalink]

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04 Mar 2019, 20:42
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]

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05 Mar 2019, 07:21
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
Re: The value of (-89)^(1/3) is:   [#permalink] 05 Mar 2019, 07:21
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