SqrtBox[x] represents in input and output.
Inside \( ... \) SqrtBox[x] can be input as \@ x.
In a notebook a SqrtBox can be created using 2 or @. moves out from under the square root sign.
In StandardForm and InputForm, SqrtBox[x] is interpreted on input as Sqrt[x].
The baseline of SqrtBox[x] is taken to be the baseline of x.
If SqrtBox[x] does not fit on a single line, it is output as x^(1/2).
In StandardForm, explicit SqrtBox objects are output literally. You can use DisplayForm to see the display form of such objects.
See The Mathematica Book: Section 2.8.10.
See also: RadicalBox, OverscriptBox.