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Which two integers is $\sqrt[3]{92}$ between? $\newline$ Choices: $\newline$ (A) $1$ and $2$ $\newline$ (B) $5$ and $6$ $\newline$ (C) $7$ and $8$ $\newline$ (D) $4$ and $5$

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Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{92}

between?

\newline

Choices:

\newline

(A)

1

and

2

\newline

(B)

5

and

6

\newline

(C)

7

and

8

\newline

(D)

4

and

5

Calculate perfect cubes: Calculate the perfect cubes near $92$ to find the range for the cube root. $\newline$ The perfect cube just below $92$ is $64$ ( $4^3 = 64$ ). $\newline$ The perfect cube just above $92$ is $125$ ( $5^3 = 125$ ).
Determine cube roots: Determine the cube roots of $64$ and $125$ .\ Cube root of $64$ is $4$ .\ Cube root of $125$ is $5$ .
Compare with cube roots: Compare $92$ with these cube roots. $\newline$ Since $64 < 92 < 125$ , it follows that $4 < \text{cube root of } 92 < 5$ .

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