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Which two integers is $\sqrt[3]{16}$ between? $\newline$ Choices: $\newline$ (A) $5$ and $6$ $\newline$ (B) $16$ and $17$ $\newline$ (C) $6$ and $7$ $\newline$ (D) $2$ and $3$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{16}

between?

\newline

Choices:

\newline

(A)

5

and

6

\newline

(B)

16

and

17

\newline

(C)

6

and

7

\newline

(D)

2

and

3

Identify perfect cubes: Step $1$ : Identify the perfect cubes near $16$ . The perfect cube just below $16$ is $8$ ( $2^3 = 8$ ). The perfect cube just above $16$ is $27$ ( $3^3 = 27$ ).
Calculate cube root of $8$ : Step $2$ : Calculate the cube root of $8$ . $2 \times 2 \times 2 = 8$ Cube root of $8$ is $2$ .
Calculate cube root of $27$ : Step $3$ : Calculate the cube root of $27$ . $\newline$ $3 \times 3 \times 3 = 27$ $\newline$ Cube root of $27$ is $3$ .
Determine cube root of $16$ : Step $4$ : Determine between which integers the cube root of $16$ falls. $\newline$ Since $2^3 = 8$ and $3^3 = 27$ , and $16$ is between $8$ and $27$ , $\newline$ The cube root of $16$ is between $2$ and $3$ .

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