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Which two integers is $\sqrt[3]{44}$ between? $\newline$ Choices: $\newline$ (A) $1$ and $2$ $\newline$ (B) $2$ and $3$ $\newline$ (C) $14$ and $15$ $\newline$ (D) $3$ and $4$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{44}

between?

\newline

Choices:

\newline

(A)

1

and

2

\newline

(B)

2

and

3

\newline

(C)

14

and

15

\newline

(D)

3

and

4

Identify perfect cubes near $44$ : Step $1$ : Identify the perfect cubes near $44$ . Find the perfect cubes just below and just above $44$ . The perfect cube just below $44$ is $27$ ( $3^3 = 27$ ). The perfect cube just above $44$ is $64$ ( $4^3 = 64$ ).
Calculate cube roots: Step $2$ : Calculate the cube roots of $27$ and $64$ . $\newline$ Cube root of $27$ is $3$ . $\newline$ Cube root of $64$ is $4$ .
Determine position of cube root: Step $3$ : Determine the position of cube root of $44$ . Since $27 < 44 < 64$ , then $3 < \text{cube root of } 44 < 4$ .

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