Chapter 4, Problem 59CR

To determine

To estimate the cube root to the nearest integer.

Answer to Problem 59CR

The best integer estimate for $\sqrt[3]{415}$ is $7$ .

Explanation of Solution

Given information:

The given expression is:

  $\sqrt[3]{415}$

Calculation:

The largest perfect cube less than $415$ is $343$ .

The smallest perfect cube greater than $415$ is $512$ .

The cube root of $415$ is between integers $\text{7 and 8}$ .

Plot the cube root on a number line:

  

Since, $415$ is closer to $343$ than to $512$ .

Hence, the best integer estimate for $\sqrt[3]{415}$ is $7$ .