I noticed that the heights of \sqrt{1}
and \sqrt{-1}
are different. For instance, when they are in between \left(
and \right)
parentheses, I must write a character of zero-width (e.g. \sqrt{-1\mathstrut}
).
Why do \sqrt{1}
and \sqrt{-1}
behave so different?
This is an example with a slightly more complicated expression:
\documentclass[]{article}
\begin{document}
$$ \left( 10 + \sqrt{7}\, \right)^{1/3} $$
$$ \left( 10 + \sqrt{-7}\, \right)^{1/3} $$
$$ \left( 10 + \sqrt{+7}\, \right)^{1/3} $$
\end{document}
The following image shows the output of latex
. I obtain similar results with pdflatex
, xelatex
and lualatex
. Notice that \sqrt{+7}
behaves as \sqrt{-7}
, but different from \sqrt{7}
.
Best Answer
You can see that in the case of
\sqrt{-1}
the radical sign is a bit lower; if you do\sqrt{\smash{-}1}
, the result will be the same.This happens because the
-
character has a depth (equal to that of+
).On the other hand, you shouldn't use
\left
and\right
in those cases. Note\,
to space a bit the closing parenthesis.More details. The character
+
extends below the baseline, so Knuth decided that-
(in math mode, the minus sign) should share the same dimensions as+
. This is true for the Computer Modern fonts, and may not be the case with other fonts.This way, the two formulas
$a+b$
and$a-b$
have the same height and depth, but1
and-1
don't: the latter has nonzero depth.The radical sign is placed so it is vertically balanced with respect to the subformula it has to cover and, indeed, it is higher in
\sqrt{1}
than in\sqrt{-1}
. This difference is sufficient for triggering a bigger size of the parentheses in the former case.