#3327 "Simplify Radicals" needs to be improved

[cheesecracker]

I just tried to simplify (4+sqrt(3))/(5-sqrt(3)); but there is a radical in the denominator in the answer.

Tried
load("sqdnst")$
sqrtdenest((4+sqrt(3))/(5-sqrt(3)));
but it does not help.

https://youtu.be/YMny-hM1NNA?t=17m17s
"No square root in the bottom" should be considered as the canonical form of simplified expression.

build_info
version="5.40.0",timestamp="2017-06-01 18:54:32",host="x86_64-w64-mingw32",lisp_name="CLISP",lisp_version="2.49 (2010-07-07) (built on toshiba [192.168.43.206])"

[David Scherfgen]

Use ratsimp(...), algebraic:

(%i1)   ratsimp((4+sqrt(3))/(5-sqrt(3))),algebraic;
(%o1)   (3^(5/2)+23)/22