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Which two integers is $\sqrt[3]{5}$ between? $\newline$ Choices: $\newline$ (A) $1$ and $2$ $\newline$ (B) $5$ and $6$ $\newline$ (C) $4$ and $5$ $\newline$ (D) $8$ and $9$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{5}

between?

\newline

Choices:

\newline

(A)

1

and

2

\newline

(B)

5

and

6

\newline

(C)

4

and

5

\newline

(D)

8

and

9

Calculate perfect cubes: Calculate the perfect cubes near $5$ . The perfect cube just below $5$ is $1$ ( $1^3 = 1$ ), and the perfect cube just above $5$ is $8$ ( $2^3 = 8$ ).
Determine cube roots: Determine the cube roots of these perfect cubes. The cube root of $1$ is $1$ , and the cube root of $8$ is $2$ .
Compare cube roots: Compare these cube roots to find where the cube root of $5$ falls. Since $1^3 = 1$ and $2^3 = 8$ , the cube root of $5$ must be between $1$ and $2$ .

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