# \sqrt too long for one line [duplicate]

I have a very long SQRT() equation, that doesn't fit in a line. I couldn't simplify it, since it involves terms in addition. Is there an alternative way to represent a root as 'SQRT{some function}' ?

\documentclass{article}
\begin{document}
$$\Delta\sigma_{V,ij} = \sqrt{\Delta\sigma_{x,ij}^2 + \Delta\sigma_{y,ij}^2 + \Delta\sigma_{z,ij}^2 - (\Delta\sigma_{x,ij}\cdot\Delta\sigma_{y,ij} + \Delta\sigma_{y,ij}\cdot\Delta\sigma_{z,ij} + \Delta\sigma_{z,ij}\cdot\Delta\sigma_{x,ij}) + 3 \cdot (\Delta\tau_{xy,ij}^2 + \Delta\tau_{yz,ij}^2 + \Delta\tau_{zx,ij}^2)}$$
\end{document}

• As written, this doesn't sound like a TeX question but one of notation. I could generally get away with saying "$y=\sqrt f(x)$ where $f(x)=...$", but I don't know if you could. – Chris H Oct 21 '19 at 7:44
• I edited the title to be more clear. – Dr. Manuel Kuehner Oct 21 '19 at 8:33

For details, see How continue a equation next line.

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\begin{equation*}
\Delta\sigma_{V,ij} = \sqrt{\Delta\sigma_{x,ij}^2 + \Delta\sigma_{y,ij}^2 + \Delta\sigma_{z,ij}^2 - (\Delta\sigma_{x,ij}\cdot\Delta\sigma_{y,ij} + \Delta\sigma_{y,ij}\cdot\Delta\sigma_{z,ij} + \Delta\sigma_{z,ij}\cdot\Delta\sigma_{x,ij}) + 3 \cdot (\Delta\tau_{xy,ij}^2 + \Delta\tau_{yz,ij}^2 + \Delta\tau_{zx,ij}^2)}
\end{equation*}

% https://tex.stackexchange.com/questions/364116/
\begin{equation*}
\Delta\sigma_{V,ij} =
\sqrt{\begin{multlined}[b]
\Delta\sigma_{x,ij}^2 + \Delta\sigma_{y,ij}^2 + \Delta\sigma_{z,ij}^2 - \\
(\Delta\sigma_{x,ij}\cdot\Delta\sigma_{y,ij} + \Delta\sigma_{y,ij}\cdot\Delta\sigma_{z,ij} + \Delta\sigma_{z,ij}\cdot\Delta\sigma_{x,ij}) + \\
3 \cdot (\Delta\tau_{xy,ij}^2 + \Delta\tau_{yz,ij}^2 + \Delta\tau_{zx,ij}^2)
\end{multlined}}
\end{equation*}

\end{document}


I'd remove the square root sign altogether:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\Diff}{\mathop{}\!\Delta}

\begin{document}

$$\begin{split} \Diff\sigma_{V,ij} =\Bigl( & \Diff\sigma_{x,ij}^2 + \Diff\sigma_{y,ij}^2 + \Diff\sigma_{z,ij}^2 \\ &- \bigl(\Diff\sigma_{x,ij}\Diff\sigma_{y,ij} + \Diff\sigma_{y,ij}\Diff\sigma_{z,ij} + \Diff\sigma_{z,ij}\Diff\sigma_{x,ij}\bigr) \\ &+ 3\bigl(\Diff\tau_{xy,ij}^2 + \Diff\tau_{yz,ij}^2 + \Diff\tau_{zx,ij}^2\bigr) \Bigr)^{\!1/2} \end{split}$$

$$\begin{split} \bigl(\Diff\sigma_{V,ij})^2 ={}& \Diff\sigma_{x,ij}^2 + \Diff\sigma_{y,ij}^2 + \Diff\sigma_{z,ij}^2 \\ &- \bigl(\Diff\sigma_{x,ij}\Diff\sigma_{y,ij} + \Diff\sigma_{y,ij}\Diff\sigma_{z,ij} + \Diff\sigma_{z,ij}\Diff\sigma_{x,ij}\bigr) \\ &+ 3\bigl(\Diff\tau_{xy,ij}^2 + \Diff\tau_{yz,ij}^2 + \Diff\tau_{zx,ij}^2\bigr) \end{split}$$

\end{document}


With \Diff you need no \cdot, as the spacing will suffice.

I propose to split the square root symbol over two lines with a hack, in two variants:

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{mathtools, nccmath}
\usepackage{dashrule}

\begin{document}

\begin{fleqn}[1em]
$$\begin{split} \\[-1ex] & Δ\sigma_{V,ij} = \\ &\begin{multlined}[0.9\linewidth] √{Δ\sigma_{x,ij}² + Δ\sigma_{y,ij}² + Δ\sigma_{z,ij}² - (Δ\sigma_{x,ij} · \Delta\sigma_{y,ij} + Δ\sigma_{y,ij} · \Delta\sigma_{z,ij} + Δ\sigma_{z,ij} · \Delta\sigma_{x,ij})} \\[0.5ex] \overline{\rule{0pt}{2.4ex}+ 3 · (Δ\tau_{xy,ij}² + Δ\tau_{yz,ij}² + Δ\tau_{zx,ij}²)} \end{multlined} \end{split}$$

$$\begin{split} \\[-1ex] & Δ\sigma_{V,ij} = \\ &\begin{multlined}[0.9\linewidth] √{Δ\sigma_{x,ij}² + Δ\sigma_{y,ij}² + Δ\sigma_{z,ij}² - (Δ\sigma_{x,ij} · \Delta\sigma_{y,ij} + Δ\sigma_{y,ij} · \Delta\sigma_{z,ij} + Δ\sigma_{z,ij} · \Delta\sigma_{x,ij})}\hdashrule[2.66ex]{1.8em}{0.4pt}{2pt} \\[0.5ex] {\hdashrule[2.67ex]{1.8em}{0.4pt}{2pt}}\mkern -4mu\overline{\rule{0pt}{2.4ex}+ 3 · (Δ\tau_{xy,ij}² + Δ\tau_{yz,ij}² + Δ\tau_{zx,ij}²)} \end{multlined} \end{split}$$
\end{fleqn}

\end{document}


• +1: \overline-magic :) – Dr. Manuel Kuehner Oct 21 '19 at 8:48
• but would a reader understand this? (I am not sure I would have understood this without the context of the question to say what the argument of the sqrt is) – David Carlisle Oct 21 '19 at 8:55
• @DavidCarlisle: I think it's self-explaining, as long as it does not interfere with notations like complex conjugation. That's the way I used from high school with paper and pencil when necessary, so I thought it rather natural. We also might add dots at the end of the square root symbol and before the overline. – Bernard Oct 21 '19 at 9:48
• I would like to propose the use of \surd and also provide a vertically extensible version for use in displayed maths. – Peter Wilson Oct 21 '19 at 17:58
• @DavidCarlisle: Following the lines sketched in my previous comment, I've added a variant which hopefully would be clearer to readers. – Bernard Oct 21 '19 at 19:07