Answer
The solution is $r=8$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt[3]{r+19}=3$
Cube each side of the equation.
$\Rightarrow (\sqrt[3]{r+19})^3=3^3$
Simplify.
$\Rightarrow r+19=27$
Subtract $19$ from each side.
$\Rightarrow r+19-19=27-19$
Simplify.
$\Rightarrow r=8$
Check $r=8$.
$\Rightarrow \sqrt[3]{r+19}=3$
$\Rightarrow \sqrt[3]{8+19}=3$
$\Rightarrow \sqrt[3]{27}=3$
$\Rightarrow \sqrt[3]{3^3}=3$
$\Rightarrow 3=3$
True.
Hence, the solution is $r=8$.
