# Splitting an equation with a long square root

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}
$$\text{RBE}(LET_d,D,(\alpha /\beta)_{phot}) = \frac{1}{2D}\cdot \left(\sqrt{\left(\frac{\alpha}{\beta}\right)_{phot}^2+4D\left(\frac{\alpha} {\beta}\right)_{phot}\left(p_0+\frac{p_1}{(\alpha/\beta)_{phot}}\cdot LET_D\right)+4D^2\left(p_2+p_3\sqrt{\left(frac{\alpha}{\beta}\right)_{phot}} \cdot LET_d\right)^2} -\left(\frac{\alpha}{\beta}\right)_{phot}\right)$$
\end{document}


And it looks like this:

• Welcome to TeX - LaTeX! There are two approaches (a) introduce symbols for subexpressions (b) use building blocks such as aligned from the amsmath package that you already load. Commented Jun 6, 2017 at 14:13
• ,@moriambar -- I don't think the duplicate you raised is relevant here because the real problem in the current question is how to split a long square root. Commented Jun 6, 2017 at 17:48
• Commented Jun 6, 2017 at 18:20

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 \\

• You should really use \textit{phot} to get better spacing, though the difference is barely visible in this particular case. Commented Jun 6, 2017 at 14:45