How to reduce size of my equation to fit properly in my beamer presentation slide?

Question

I am preparing slides using beamer. However, my equation has exceeded the page margin. I have tried several solutions given on this website, but with those solutions, my .tex file is not compiling. Here is the code of my original beamer slide:

\documentclass{beamer}
\usepackage[english]{babel}
\usefonttheme[onlymath]{serif}
\usepackage{color}
\usepackage{graphicx}
\usepackage{amssymb,amsmath}
\usepackage{tikz}
\usepackage{epstopdf}
\begin{document}

\begin{frame}

\begin{itemize}

\item whenever $k$ is of the form $2^i$, where $i\in\mathbb{N}$, then

\begin{equation}
0.5(\sqrt[3]{n+\sqrt{n^2-1/27}}+ \sqrt[3]{n-\sqrt{n^2-1/27}})
\leq k < 0.125 (\sqrt{n}+\sqrt{n+16(\sqrt{n}+1)})
\end{equation}

\end{itemize}

\end{frame}

\end{document}

And I am getting the following output:

Please help me resolve this issue!

Answer 1

I suggest you make two, separate changes. First, use an environment such as multline instead of equation to make it possible to introduce a line break right before \leq k. Second, use \Bigl( and \Bigr) for the "outer" parentheses in both rows.

\documentclass{beamer}
\usefonttheme[onlymath]{serif}

\begin{document}
\begin{frame}
\begin{itemize}

\item If $k$ is of the form $2^i$, where $i\in\mathbb{N}$, then
\begin{multline}
0.5\Bigl(\sqrt[3]{n+\sqrt{n^2-1/27}}+ \sqrt[3]{n-\sqrt{n^2-1/27}}\,\Bigr) \\
\leq k < 0.125 \Bigl(\sqrt{n}+\sqrt{n+16(\sqrt{n}+1)}\,\Bigr)
\end{multline}

\end{itemize}
\end{frame}
\end{document}