Memo for the moderator.
Sorry, I am new to "Ask a question". Is my writing correct ? Shall I receive a reply directly to my e-mail address or somewhere in the StackExchange?
My question: I want to simplify the following expression, when $-1 < x < 1$ and $-1 < y < 1$,
sol = Sqrt[1/(x + Sqrt[x^2 + y^2])].
By hand I obtain
sol$rat = Sqrt[(-x + Sqrt[x^2 + y^2])/y^2]
but, as I have not been able to find a built-in command, I have tried naively, without success after several tests
rational$sol = Sqrt[1/((x + Sqrt[x^2 + y^2]) (-x + Sqrt[x^2 + y^2]))*(-x + Sqrt[ x^2 + y^2])] // FullSimplify
When I search (e.g., stack exchange ...) "Simplifying Radicals in Numerator and Denominator - Mathematica," I see no satisfying solution.