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

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

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Re: The value of (-89)^(1/3) is: [#permalink]
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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 $$-5$$

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