To answer my own question (and clarify what I meant), no:

```
In [4]: sqrtdenest2((1 + sqrt(625 - 29*sqrt(5)))*sqrt(5 + sqrt(5)), full=True)
Out[4]:
⎛       __________________⎞    ___________
⎜      ╱        ___       ⎟   ╱   ___
⎝1 + ╲╱  - 29⋅╲╱ 5  + 625 ⎠⋅╲╱  ╲╱ 5  + 5
```