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Which two integers is $\sqrt[3]{124}$ between? $\newline$ Choices: $\newline$ (A) $0$ and $1$ $\newline$ (B) $9$ and $10$ $\newline$ (C) $4$ and $5$ $\newline$ (D) $7$ and $8$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{124}

between?

\newline

Choices:

\newline

(A)

0

and

1

\newline

(B)

9

and

10

\newline

(C)

4

and

5

\newline

(D)

7

and

8

Identify perfect cubes: Step $1$ : Identify the perfect cubes near $124$ . $\newline$ We know that $5^3 = 125$ and $4^3 = 64$ . Since $64$ is less than $124$ and $125$ is just above $124$ , the cube root of $124$ must be between the cube roots of $64$ and $125$ .
Calculate cube roots: Step $2$ : Calculate the cube roots of $64$ and $125$ . $\newline$ The cube root of $64$ is $4$ because $4^3 = 64$ . $\newline$ The cube root of $125$ is $5$ because $5^3 = 125$ .
Determine integer range: Step $3$ : Determine between which integers the cube root of $124$ falls. $\newline$ Since $4^3 < 124 < 5^3$ , it follows that $4 < \sqrt[3]{124} < 5$ .

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