# 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?

Let us see an example where also `R.simplify_chain_real()`

messes things up:

```
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 = p1*p2*sqrt(p3)*sqrt(p3/p1)*sqrt(p3/p2)/((p1 - p3)*(p2 - p3)*(p3 - 1))
%display latex
from sage.manifolds.utilities import simplify_chain_real
simplify_chain_real(R)
#R
```

what is

`simplify_chain_real`

? Not in Sagemath 9.1.beta0...One has to import it:

It is documented here

Indeed,

`simplify_chain_real`

does the job here:On general grounds, for real expressions,

`simplify_chain_real`

is safer than`canonicalize_radical`

(see the doc examples for a case where`canonicalize_radical`

yields a wrong result).@eric_g I understand, but still

`simplify_chain_real`

messes things up, look at the second example I added.