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Which two integers is $\sqrt[3]{10}$ between? $\newline$ Choices: $\newline$ (A) $12$ and $13$ $\newline$ (B) $2$ and $3$ $\newline$ (C) $0$ and $1$ $\newline$ (D) $13$ and $14$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{10}

between?

\newline

Choices:

\newline

(A)

12

and

13

\newline

(B)

2

and

3

\newline

(C)

0

and

1

\newline

(D)

13

and

14

Identify Perfect Cubes: Identify the perfect cubes near $10$ . The perfect cube just below $10$ is $8$ ( $2^3 = 8$ ). The perfect cube just above $10$ is $27$ ( $3^3 = 27$ ).
Calculate Cube Roots: Calculate the cube root of $8$ . $\newline$ Since $2^3 = 8$ , the cube root of $8$ is $2$ .
Determine Range: Calculate the cube root of $27$ . $\newline$ Since $3^3 = 27$ , the cube root of $27$ is $3$ .
Determine Range: Calculate the cube root of $27$ . Since $3^3 = 27$ , the cube root of $27$ is $3$ . Determine between which integers the cube root of $10$ falls. Since $2 < \text{cube root of } 10 < 3$ , the cube root of $10$ is between $2$ and $3$ .

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