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intransigent root expressions

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg616] intransigent root expressions
• From: wmm at chem.wayne.edu (Martin McClain)
• Date: Wed, 29 Mar 95 11:39:52 EST

Dear MathGroupers:
In solving scientific problems you often run across expressions like

In[181]:=
xSolns = Solve[2.*10^-25 y==3.*10^-25 x^2+7.*10^-26, x]

where the large exponents are generated by the SI unit system applied to
atomic scale quantities.  Using Solve, and extracting the answer, the
positive solution comes out as

  xExpr = 5.54977*10^-25 * Sqrt[-7.57576*10^47 + 2.16450*10^48*y]

This would be your answer, if only you could force that tiny exterior
coefficient to multiply into the huge numbers under the square root.

Does anybody know a graceful way to do this?  

The operators Expand, ExpandAll, Simplify, and PowerExpand all leave it
unchanged.  ComplexExpand makes it worse.  My current solution, which I
feel is far too complicated for this simple desire, is

In[183]:=
x -> Sqrt[xExpr /. m_ Sqrt[n_]->m^2 n // Expand]

Out[183]=
x -> Sqrt[-0.233333 + 0.666667 y]