Chapter A.10, Problem 4AYU

To determine

Check whether the given statement is true or false.

Answer to Problem 4AYU

It is a true statement.

Explanation of Solution

Given:

Statement says that $\sqrt[5]{-32}=-2$.

Calculation:

If $n\ge 2$ is an integer and $a$ is a real number, then

$\sqrt[n]{a^n}=a$ if $n\ge 3$ is odd.

$\sqrt[n]{a^n}=\left|a\right|$ if $n\ge 2$ is even.

$\sqrt[5]{-32}=\sqrt[5]{{\left(-2\right)}^5}=-2$, since 5 is odd.