Chapter 4, Problem 58CR

To determine

To estimate the cube root to the nearest integer.

Answer to Problem 58CR

The best integer estimate for $\sqrt[3]{90}$ is $4$ .

Explanation of Solution

Given information:

The given expression is:

  $\sqrt[3]{90}$

Calculation:

The largest perfect cube less than $90$ is $64$ .

The smallest perfect cube greater than $90$ is $125$ .

The cube root of $90$ is between integers $4\text{ and }5$ .

Plot the cube root on a number line:

  

Since, $90$ is closer to $64$ than to $125$ .

Hence, the best integer estimate for $\sqrt[3]{90}$ is $4$ .