If there were no argument to the macro, this would be just a matter of loading the
newunicodechar package or using the
\DeclareUnicodeCharacter macro. For the "character" to accept arguments, a slightly different approach is needed.
If you use XeTeX or LuaTeX, you can use either of
(The second approach is more robust.)
With pdfTeX the
\√ syntax will not work because of the way pdfTeX handles input (it is theoretically possible to achieve this, though). This leaves the only way (taken and modified from