Since I am on lockdown,
I have time to look at some old questions that had been put aside for a rainy day.
Here is one.
Maybe someone other than me might be interested ....
https://web2.0calc.com/questions/let-x-4-over-sqrt5-1-root-4-of5-1-root-8-of5-1-root
I answered the question at the original thread, maybe my solution is not the best, but I hope it would be helpful.