I am currently doing some investigations on *Sylvester's 4 Point Problem* [Probability of 4 Points being in Convex Configuration](https://mathoverflow.net/questions/166228/probability-of-4-points-being-in-convex-configuration)
and repeatedly face the problem of solving equations between sums of euclidean distances between points, of which a typical example is $$\sqrt{(x\_B-x\_A)^2+(y\_B-y\_A)^2}+\sqrt{(x\_D-x\_C)^2+(y\_D-y\_C)^2}=\sqrt{(x\_C-x\_A)^2+(y\_C-y\_A)^2}+\sqrt{(x\_D-x\_B)^2+(y\_D-y\_B)^2}$$  

where the subscripts denote the point, to which the subscripted coordinate refers. 


while it is possible to remove the square roots in that example manually by repeated squaring, it is tedious and error prone and, if there are more than two square roots on each side, then I think repeated squaring won't work. 



> 
> **Question:** 
> 
> 
> are there any free online tools, that convert an equation with radicals into an algebraic one? 
> 
> 
> 


My searches in the internet only brought up a haystack of solvers for trivial instances (from the perspective of what I need).



Tools for Removing Radicals from Equations
I don't know about "free", but the general solution is to introduce a variable for each radical, together with an equation $y^2 = f(x),$ and then solve the resulting system. Since this is easy to do in Mathematica, I assume WolframAlpha will do it for you for free, but I never use WA, so can't promise.


