To me, the expression
SqrtSqrt[x] is more complex than
Sqrt[2x]. But even if I merely input the latter, I get the former as output. I'd like to simplify expressions where such square roots could get additional terms inside, so
Defer don't really help. See e.g. this:
FullSimplify[Sqrt[2 x] Sqrt[y], x > 0 && y > 0]
This gives me
Sqrt Sqrt[x y] as a result, while I'd prefer
Sqrt[2 x y]. Even if I specify complexity function like the following, it still doesn't help:
FullSimplify[Sqrt[2 x] Sqrt[y], x > 0 && y > 0, ComplexityFunction -> (Times@@ImageDimensions@Rasterize[#] &)]
And this is despite these results:
Times@@ImageDimensions@Rasterize[Sqrt[2 x]] Times@@ImageDimensions@Rasterize[HoldForm[Sqrt[2 x]]]
I've looked at
SystemOptions["SimplificationOptions"], but haven't found anything related to this type of simplification.
Is there any way to prevent such splitting of constants from the radical?