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, but`1`

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.