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Which two integers is $\sqrt[3]{24}$ between? $\newline$ Choices: $\newline$ (A) $2$ and $3$ $\newline$ (B) $0$ and $1$ $\newline$ (C) $10$ and $11$ $\newline$ (D) $4$ and $5$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{24}

between?

\newline

Choices:

\newline

(A)

2

and

3

\newline

(B)

0

and

1

\newline

(C)

10

and

11

\newline

(D)

4

and

5

Calculate Range: Calculate the perfect cubes near $24$ to find the range for the cube root. $\newline$ $8$ ( $2^3$ ) is below $24$ , and $27$ ( $3^3$ ) is above $24$ .
Find Cube Root of $8$ : Determine the cube root of $8$ . $\newline$ Cube root of $8$ is $2$ .
Find Cube Root of $27$ : Determine the cube root of $27$ . $\newline$ Cube root of $27$ is $3$ .
Compare Cube Roots: Compare $24$ with the cube roots found. $\newline$ Since $24$ is between $8$ and $27$ , its cube root must be between $2$ and $3$ .

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