Large Square Root Symbols

Question

Normally the \sqrt{x} symbol automatically scales according to x, so that it usually seems to be the right size.

But is there any way to manually increase the size of one instance of the \sqrt symbol?

This issue came up in the following MWE:

\documentclass{article}
\newcommand{\blank}[1]{\hfil\penalty1000\hfilneg\rule[-3pt]{#1}{0.4pt}} % nice blank underscores
\begin{document}
Fill in the blank for the following equation:
\[ 3 = \sqrt{\blank{1cm}} \]
\end{document}

Answer 1

Perhaps a strut is what you are looking for:

\documentclass{article}
\newcommand{\blank}[1]{\hfil\penalty1000\hfilneg\rule[-3pt]{#1}{0.4pt}} % nice blank underscores
\begin{document}
Fill in the blank for the following equation:
\[ 3 = \sqrt{\blank{1cm}} \]
\[ 3 = \sqrt{\strut\blank{1cm}} \]
\end{document}

A strut is a zero width rule the height of a bracket in the current font, TeX formats tend to insert them in various places like table rows to ensure that things get an even spacing. More exactly LaTeX defines strut as

\def\strut{\relax\ifmmode\copy\strutbox\else\unhcopy\strutbox\fi}

Where \strutbox is (re)defined whever there is a size-changing command by the following code:

\setbox\strutbox\hbox{%
  \vrule\@height.7\baselineskip
        \@depth.3\baselineskip
        \@width\z@}%

\z@ means 0pt.

Answer 2

The \phantom{<stuff>} command places a box of horizontal width and vertical height equivalent to the contents <stuff>. It has two smaller equivalents \hphantom and \vphantom that are respectively the horizontal and vertical components of the contents only:

\documentclass{article}
\newcommand{\blank}[1]{\hfil\penalty1000\hfilneg\rule[-3pt]{#1}{0.4pt}} % nice blank underscores
\begin{document}
Fill in the blank for the following equation:
\[ 3 = \sqrt{\blank{1cm}} \]
\[ 3 = \sqrt{\vphantom{\sum}\blank{1cm}} \]
\end{document}

Of course, another alternative would be to place a zero-width rule \rule{0pt}{<height>} of arbitrary height, which acts just like \vphantom, and just like a \strut.