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I am writing in IEEEtran two-column environment and has a display formula like this sqrt{frac{1^{2}}{0.111222}(0.111222times1.111163+0.066987^{2}times0.111222)-1}=sqrt{0.111222}=0.111222. Before the first equal sign is a long square root. This square root is just a little bit wider than the column. Is there a way I can squeeze the square root within the column as a first line and put the rest beginning with the "=" as a second line?

The answer is yes. Here's an illustration (followed by an explanation).

documentclass{IEEEtran}



usepackage{amsmath}



newcommand*squeezespaces[1]{% %% <- #1 is a number between 0 and 1

  thickmuskip=scalemuskip{thickmuskip}{#1}%

  medmuskip=scalemuskip{medmuskip}{#1}%

  thinmuskip=scalemuskip{thinmuskip}{#1}%

  nulldelimiterspace=#1nulldelimiterspace

  scriptspace=#1scriptspace

}

newcommand*scalemuskip[2]{%

  muexpr #1*numexprdimexpr#2ptrelaxrelax/65536relax

} %% <- based on  https://tex.stackexchange.com/a/198966/156366



begin{document}



This is a long equation This is a long equation This is a long equation

This is a long equation This is a long equation This is a long equation

[ %% vv Unaltered vv

    sqrt{frac{1^{2}}{0.111222}

      (0.111222times1.111163+0.066987^{2}times0.111222)-1}

    = sqrt{0.111222}=0.111222

]

This is a long equation This is a long equation This is a long equation

This is a long equation This is a long equation This is a long equation

[ %% vv Squeezed and split vv

    begin{split}                  %% <- split up equation, &'s will be aligned

        kern 4em & kern-4em      %% <- move anchor right by 4em

        mbox{$squeezespaces{0.5} %% <- reduce whitespace, switch to textstyle

          sqrt{frac{1^{2}}{0.111222}

          (0.111222times1.111163+0.066987^{2}times0.111222)-1}

        $}

        \&

          = sqrt{0.111222}

        \&                        %% <- leave this out if you want

          = 0.111222

    end{split}

]

This is a long equation This is a long equation This is a long equation

This is a long equation This is a long equation This is a long equation



end{document}

I've done the following:

1. I've used the split environment from amsmath to split up the equation in three lines. You can reduce this to two lines by removing the second \&.




2. To place the anchor (&) at the right spot, I've inserted a horizontal space in front of it and a negative horizontal space of equal magnitude after it with kern 4em & kern-4em.



3. 
   

   The amount of whitespace inserted at several places in an equation is governed by the following paramters: thickmuskip (; and space around e.g. =), medmuskip (: and space around e.g. +), thinmuskip (, and space around e.g. sum and sin), nulldelimiterspace (space around e.g. fractions) and scriptspace (space after sub-/superscripts). I've halved each of these lengths using squeezespaces{0.5} (which is defined in the preamble).

   
   
   

   Doing this affects an entire equation and it can't be done inside split, so I've put the square root inside an mbox{$<…>$} and used squeezespaces{0.5} in the inner math environment. You can replace 0.5 by another number between 0 and 1 if you want.

   
   


4. 
   

   A side-effect of putting the sqrt in a box is that it is set in textstyle, which also saves space because it makes e.g. fractions smaller. You could also have accomplished this by using tfrac instead of frac or by inserting textstyle right before sqrt (or at the beginning of its first argument).

   
   
   

   If you don't want text style fractions you should use mbox{$displaystyle<…>$}.

   
   

For the math expression you provided -- I have no idea how representative it is of the real material in your document -- it suffices to rearrange the position of the denominator in order to make the material before the = symbol fit in a column; then, use an align* environment to split the full expression across two lines.

documentclass{IEEEtran}

usepackage{amsmath} % for 'align*' env.



begin{document}

hrule % just to illustrate width of column

begin{align*}

&sqrt{frac{1^{2}(0.111222times1.111163

  +0.066987^{2}times0.111222)}{0.111222}-1}\

&quad=sqrt{0.111222}=0.111222 % place remaining material on 2nd line

end{align*}

end{document}

documentclass{IEEEtran}

usepackage{amsmath}

begin{document}



hrule



begin{align*}

&begin{aligned}[t]

Bigl[frac{1^2}{0.111222}(0.111222&times1.111163 \

     &+ 0.066987^{2}times0.111222)-1Bigr]^{frac12}

end{aligned}\

&= sqrt{0.111222} \

&= 0.111222

end{align*}



hrule



end{document}

Another option is to use 4 decimal-digits numbers (this is quite a standard in some software like MATLAB) unless these extra digits are very important.

begin{align*}

&sqrt{frac{1^2}{0.1112}(0.1112times1.1112 + 0.0670^2times0.1112)-1} \

&quad = sqrt{0.1112} \

&quad = 0.1112

end{align*}

A third option would be to give variable names like x,y,z to these values:

begin{align*}

&sqrt{frac{1^2}{x}(xtimes y + z^2times x)-1} \

&quad = sqrt{0.115650} \

&quad = 0.340074 

end{align*}

%

with $x=0.111222$, $y=1.111163$, and $z=0.066987$.

Try using split or multiline in the amsmath package. There are a couple of examples on page 2 of "Short Math Guide".

Try:

documentclass{IEEEtran}

usepackage{amsmath}



begin{document}



begin{equation}

begin{split}

sqrt{frac{1^{2}}{0.111222}(0.111222times1.111163}&\

overline{rule{0pt}{5mm}{}+0.066987^{2}times0.111222)-1}&\    

=sqrt{0.111222}=0.111222&

end{split}

end{equation}



begin{multline}

sqrt{frac{1^{2}}{0.111222}(0.111222times1.111163}\

overline{rule{0pt}{5mm}{}+0.066987^{2}times0.111222)-1}\

=sqrt{0.111222}=0.111222

end{multline}



end{document}

and adjust the 5mm in rule to get the overline spacing to look right.

Some other options to adjust the overline spacing