### how to best simplify product of square roots

I'd like to simplify expressions like

```
p1,p2,p3 = var('p1 p2 p3')
assume(p1>0,p2>0,p3>0)
R = p1*p2*sqrt(p3)*sqrt(p3/p1)*sqrt(p3/p2)
R
```

without using `R.canonicalize_radical()`

, which unfortunately messes up other factors. I understand there are some options using `R.simplify_chain_real()`

, but what else can I try?