Answer
False
Work Step by Step
We will solve the equation to see what its solution is:
Step 1: $\sqrt[3] {x+2}=-2$
Step 2: Raising each side of the equation to the power of $3$ and simplifying, we find:
$(\sqrt[3] {x+2})^{3}=(-2)^{3}$
$x+2=-8$
Step 3: Solving the equation, we find:
$x+2=-8$
$x=-8-2$
$x=-10$
Therefore, the solution set of the equation is {$-10$}, which means that the question statement is false.
