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Which two integers is $\sqrt[3]{22}$ between? $\newline$ Choices: $\newline$ (A) $[1 \text{ and } 2]$ $\newline$ (B) $[15 \text{ and } 16]$ $\newline$ (C) $[16 \text{ and } 17]$ $\newline$ (D) $[2 \text{ and } 3]$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{22}

between?

\newline

Choices:

\newline

(A)

[1 \text{ and } 2]

\newline

(B)

[15 \text{ and } 16]

\newline

(C)

[16 \text{ and } 17]

\newline

(D)

[2 \text{ and } 3]

Find Perfect Cubes: Find the perfect cubes that are just below and just above $22$ . $\newline$ The perfect cube just below $22$ is $8$ (since $2^3 = 8$ ). $\newline$ The perfect cube just above $22$ is $27$ (since $3^3 = 27$ ).
Calculate Cube Root of $8$ : Calculate the cube root of $8$ . $\newline$ $2 \times 2 \times 2 = 8$ $\newline$ $2^3 = 8$ $\newline$ The cube root of $8$ is $2$ .
Calculate Cube Root of $27$ : Calculate the cube root of $27$ . $\newline$ $3 \times 3 \times 3 = 27$ $\newline$ $3^3 = 27$ $\newline$ The cube root of $27$ is $3$ .
Determine Cube Root of $22$ : Determine between which two integers the cube root of $22$ falls. $\newline$ Since the cube root of $8$ is $2$ and the cube root of $27$ is $3$ , we can conclude that: $\newline$ $2 < \sqrt[3]{22} < 3$ $\newline$ Therefore, the cube root of $22$ falls between the integers $2$ and $3$ .

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