I can't bear an expression containing radicals of imaginary numbers, in case it can be expressed as in terms of radicals of real numbers only.
For example, I can't bear the expression
Sqrt[2 + I]
because it can be expressed as
Sqrt[1/2 (2 + Sqrt)] + Sqrt[1/2 (-2 + Sqrt)] I
But it seems there is no easy way to do it in Mathematica. I have tried many commands (in Mathematica) but all in vain.
Is there a systematic way to do such job ?
Sqrt[2 + I] was a very simple example. I hope the method work for much more complicated expression.
I know that there are many algebraic numbers that cannot be expressed as in terms of radicals, For example,
Root[#^5 + # - 1 &, 1].