How do you solve #sqrt(3 + sqrt5) -sqrt(2 + sqrt3)#?
Here I can give you only a hint (I have to go to work!).
I would use a technique called "denesting";
You can write:
You square both sides:
And you put:
You must now solve this system in
You should get:
Try substituring in your original expression and eventually rationalize.
PLEASE check my numbers and operations because I did them in a hurry!!! :-l