What about applying PowerExpand?

In[2]:= Sqrt[PowerExpand[(Sqrt[2] - 1)^2]]

Out[2]= -1 + Sqrt[2]

In[3]:= Sqrt[PowerExpand[(Sqrt[3] - Sqrt[2])^2]]

Out[3]= -Sqrt[2] + Sqrt[3]

Dear Valeriu: PowerExpand has no effect here--you could replace it by Identity. And replacing it with Expand has the exact opposite effect of what Strad (and its verbose cousin DenestRadicals3)

In[491]:= Sqrt[Expand[(Sqrt[3] - Sqrt[2])^2]]

Out[491]= Sqrt[5 - 2 Sqrt[6]]

In[492]:= DenestRadicals3@%

During evaluation of In[492]:= {f[Sqrt[5-2 Sqrt[6]]]}

During evaluation of In

During evaluation of In[492]:= problem Sqrt[5-2 Sqrt[6]]

During evaluation of In[492]:= outer root: 2 extra root: 1

During evaluation of In

During evaluation of In[492]:= multiplier count: 2 multipliers: {1,Sqrt[6]}

During evaluation of In[492]:= multiplier: 1 minpoly degree: 4

During evaluation of In[492]:= adding new multipliers from: 1

During evaluation of In[492]:= multiplier: Sqrt[6] minpoly degree: 4

During evaluation of In[492]:= adding new multipliers from: Sqrt[6]

During evaluation of In[492]:= multiplier count: 3 from: {1,4}

During evaluation of In[492]:= multiplier: 2 minpoly degree: 2

During evaluation of In[492]:= success: {2,2,{{2,1}}}

During evaluation of In[492]:= history: {{0,[Infinity]},{1,4},{2,2}}

During evaluation of In[492]:= -Sqrt[2]+Sqrt[3]

During evaluation of In

Out[492]= -Sqrt[2] + Sqrt[3]

are trying to achieve, namely, to convert the radicand back into a power that cancels the root operation. So I don't understand the objective of PowerExpand here. --Bill