I see this interesting question here.

But I want to simplify it with the help of Simplify function (Maybe the TransformationFunctions and ComplexityFunction options will be used) . How can I reduce the expression $\sqrt{5-2 \sqrt{6}}$ to $ \sqrt{3}-\sqrt{2}$ ?

Simplify[Sqrt[5 - 2 Sqrt[6]]]

I hope to use MMA's Simplify function to achieve this simplification.


Try this:

FullSimplify[Sqrt[5 - 2 Sqrt[6]], ComplexityFunction -> (Count[#, Sqrt[6], Infinity] &)]

(*  -Sqrt[2] + Sqrt[3]   *)

Note that it works with FullSimplify but not with Simplify. I do not know the reason.

Have fun!

| improve this answer | |
  • $\begingroup$ Thank you very much. Can you use TransformationFunctions function to achieve this? $\endgroup$ – A little mouse on the pampas Feb 10 at 23:50

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