Find the integer that lies between $\sqrt[3]{-45}$ and $\sqrt[3]{-101}$

Question

Find the integer that lies between $\sqrt[3]{-45}$ and $\sqrt[3]{-101}$

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Ngọc Khuê 4 years 2021-08-06T04:44:07+00:00 1 Answers 75 views 0

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  1. Acacia
    0
    2021-08-06T04:46:05+00:00
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    ∛(-45) = ∛((-1) × 45) = ∛(-1) × ∛45 = -∛45

    Similarly,

    ∛(-101) = – ∛101

    Now,

    • 3³ = 27 and 4³ = 64, and 27 < 46 < 64, so ∛27 < ∛45 < ∛64, which places ∛45 between 3 and 4

    • 5³ = 125, so ∛101 would similarly fall between 4 and 5

    So to summarize, we have

    3 < ∛45 < 4 < ∛101 < 5

    so that

    -5 < ∛(-45) < -4 < ∛(-101) < -3

    so the integer between these numbers is -4.

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