You can find information about the history of the usage in Jeff Miller's page here: Earliest Uses of Symbols of Operation.
Square root. The first use of a
capital R with a diagonal line was in
1220 by Leonardo of Pisa in Practica
geometriae, where the symbol meant
"square root" (Cajori vol. 1, page
The radical symbol first appeared in
1525 in Die Coss by Christoff Rudolff
(1499-1545). He used the symbol
(without the vinculum) for square
roots. He did not use indices to
indicate higher roots, but instead
modified the appearance of the radical
symbol for higher roots.
It is often suggested that the origin
of the modern radical symbol is that
it is an altered letter r, the first
letter in the word radix. This is the
opinion of Leonhard Euler in his
Institutiones calculi differentialis
(1775). However, Florian Cajori,
author of A History of Mathematical
Notations, argues against this theory.
In 1637 Rene Descartes used , adding
the vinculum to the radical symbol La
Geometrie (Cajori vol. 1, page 375).