Chapter 7.3, Problem 37CCR

To determine

Find the cube root of $\sqrt[3]{-512}$

Answer to Problem 37CCR

  $\sqrt[3]{-512}=-8$

Explanation of Solution

Given: Find the cube root of $\sqrt[3]{-512}$

Concept Used:

The cube root of a number, $n^3$ , written as

  $\sqrt[3]{n^3}=\sqrt[3]{n·n·n}=n$ the number that gives n when multiplied by itself thrice

For example, $\sqrt[3]{1000}=\sqrt[3]{10·10·10}=10$ because 10 x 10 x10= 1000

A cube root of a number is a value that can be multiplied by itself thrice to give the original number.

Rule: $\sqrt[3]{n^3}=\sqrt[3]{n·n·n}=n$

Calculation:

A cube root of a number is a value that can be multiplied by itself thrice to give the original number.

Rule: $\sqrt[3]{n^3}=\sqrt[3]{n·n·n}=n$

Find the cube root of $\sqrt[3]{-512}$

  $\sqrt[3]{-512}=\sqrt[3]{-8·-8·-8}=-8$

Thus, $\sqrt[3]{-512}=-8$