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Which two integers is $\sqrt[3]{37}$ between? $\newline$ Choices: $\newline$ (A) $11$ and $12$ $\newline$ (B) $2$ and $3$ $\newline$ (C) $7$ and $8$ $\newline$ (D) $3$ and $4$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{37}

between?

\newline

Choices:

\newline

(A)

11

and

12

\newline

(B)

2

and

3

\newline

(C)

7

and

8

\newline

(D)

3

and

4

Identify perfect cubes: Step $1$ : Identify the perfect cubes near $37$ . $\newline$ We know that $3^3 = 27$ and $4^3 = 64$ . Since $27$ is less than $37$ and $64$ is greater than $37$ , the cube root of $37$ must be between the cube roots of $27$ and $64$ , which are $3$ and $4$ , respectively.
Confirm range: Step $2$ : Confirm the range. $\newline$ Since $3^3 = 27$ and $4^3 = 64$ , and $37$ is between these two values, it confirms that the cube root of $37$ is between $3$ and $4$ .

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