# How to use TransformationFunctions to simplify this expression

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.

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

Note that it works with FullSimplify but not with Simplify. I do not know the reason.
• Thank you very much. Can you use TransformationFunctions function to achieve this? Feb 10 '20 at 23:50