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Which two integers is $\sqrt[3]{38}$ between? $\newline$ Choices: $\newline$ (A) $9$ and $10$ $\newline$ (B) $13$ and $14$ $\newline$ (C) $3$ and $4$ $\newline$ (D) $6$ and $7$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{38}

between?

\newline

Choices:

\newline

(A)

9

and

10

\newline

(B)

13

and

14

\newline

(C)

3

and

4

\newline

(D)

6

and

7

Identify perfect cubes: Step $1$ : Identify the perfect cubes near $38$ . $\newline$ We know that $3^3 = 27$ and $4^3 = 64$ . Since $27$ is less than $38$ and $64$ is more than $38$ , the cube root of $38$ must be between $3$ and $4$ .
Calculate approximate cube root: Step $2$ : Calculate the approximate cube root of $38$ . $\newline$ Since $3^3 = 27$ and $4^3 = 64$ , we can estimate the cube root of $38$ to be closer to $3$ because $38$ is nearer to $27$ than to $64$ .
Confirm cube root range: Step $3$ : Confirm the integers between which the cube root of $38$ falls. $\newline$ From the calculations, $3 < \sqrt[3]{38} < 4$ . Therefore, the cube root of $38$ is between the integers $3$ and $4$ .

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