Which two integers is root(3) 38 between? Choices: (A)9 and 10 (B)13 and 14 (C)3 and 4 (D)6 and 7

Identify perfect cubes: Step 1: Identify the perfect cubes near 38. 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. 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. 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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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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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 $4$ .