[Tex/LaTex] How to break this long radical into multiple lines

line-breakingmath-mode

I've got a very long radical in a display-math environment, so long that the equation spills in the right margin. How can I break that equation over multiple lines, so that it doesn't go into the right margin?

enter image description here

\documentclass[12pt,a4paper]{article}

\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{fourier}
\usepackage[left=3cm,right=3cm,top=2.5cm,bottom=2cm]{geometry}

\begin{document}
\[
    V_{DABC}=\dfrac{1}{6}\cdot DA \cdot DB \cdot DC \cdot \sqrt{1+2\cdot
    \cos \widehat{ADB}\cdot \cos \widehat{BDC}\cdot \cos \widehat{ADC}
    -\cos^2 \widehat{ADB} -\cos^2 \widehat{ADC} -\cos^2 \widehat{BDC}} 
    =\dfrac{2\sqrt{2}}{3}.
\]
\end{document}

Best Answer

I'd much prefer Jubobs's approach, but just to show another method, you can split into two lines the radicand:

\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{fourier}
\usepackage[left=3cm,right=3cm,top=2.5cm,bottom=2cm]{geometry}
\begin{document}
\[
  V_{DABC}=\dfrac{1}{6}\cdot DA \cdot DB \cdot DC \cdot
  \sqrt{
    \begin{aligned}
     1+&2\cos\widehat{ADB}\cos\widehat{BDC}\cos\widehat{ADC} \\
     & -\cos^2 \widehat{ADB} -\cos^2 \widehat{ADC} -\cos^2 \widehat{BDC}
    \end{aligned}
  }
  =\dfrac{2\sqrt{2}}{3}.
\]
\end{document}

I removed the unnecessary centered dots.

enter image description here

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