Answer
$\frac{1000}{9}$
Work Step by Step
Step 1. As $p$ varies jointly as $q$ and $r^2$, we have $p=kqr^2$ where $k$ is a constant.
Step 2. As $p=100$ when $q=2,r=3$, we have $100=k(2)(3)^2$, thus $k=\frac{50}{9}$
Step 3. For $q=5,r=2$, we have $p=\frac{50}{9}(5)(2)^2=\frac{1000}{9}$
