[Tex/LaTex] Splitting an equation with a long square root

Question

I want to split up a very long equation. Here is my code:

\documentclass[11pt,a4paper,oneside,onecolumn,article]{memoir}
\usepackage[latin1]{inputenc}
\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{amsfonts}
\begin{document}
\begin{equation}
\text{RBE}(LET_d,D,(\alpha /\beta)_{phot}) = \frac{1}{2D}\cdot
\left(\sqrt{\left(\frac{\alpha}{\beta}\right)_{phot}^2+4D\left(\frac{\alpha}
{\beta}\right)_{phot}\left(p_0+\frac{p_1}{(\alpha/\beta)_{phot}}\cdot
LET_D\right)+4D^2\left(p_2+p_3\sqrt{\left(frac{\alpha}{\beta}\right)_{phot}}
\cdot LET_d\right)^2}
-\left(\frac{\alpha}{\beta}\right)_{phot}\right)
\end{equation}
\end{document}

And it looks like this:

Thank you in advance!

Answer 1

Making use of the multline environment and exploiting the repetition of some big terms; the shortcut $\lambda=(\alpha/\beta)_{phot}$ can be used replacing \lambda with a suitable symbol if it is already used, one can do the following:

\documentclass[11pt,a4paper,oneside,onecolumn,article]{memoir} 
\usepackage{mathtools}
\usepackage{amsmath}
\begin{document}

\newcommand{\LET}{\ensuremath{\operatorname{LET}}}
\begin{multline}
\text{RBE}(\LET_d,D,\lambda) = \frac{1}{2D}\times{} \\  
\left(\sqrt{\lambda^2+4D\lambda\left(p_0+\frac{p_l}{\lambda}\cdot\LET_d\right)+4D^2\left(p_2+p_3\sqrt{\lambda}\cdot\LET_d\right)^2}-\lambda\right)
\end{multline}
%
where $\lambda=(\alpha/\beta)_{phot}$

\end{document}

Another possibility (less readable, though) is to use ()^1/2 notation for the square root:

\newcommand{\ab}{\ensuremath{\Bigl(\frac{\alpha}{\beta}\Bigr)_\text{phot}}}
\begin{align}
\text{RBE}(\LET_d,D,(\alpha/\beta)_\text{phot}) 
   &= \frac{1}{2D}\biggl[\biggl(\ab^2+4D\ab\Bigl(p_0+\frac{p_l}{(\alpha/\beta)_\text{phot}}\LET_d\Bigr) \notag \\                                                  
   &\quad+4D^2\Bigl(p_2+p_3\sqrt{\ab}\LET_d\Bigr)^2\biggr)^\frac12-\ab\biggr]
\end{align}