How did the square root get its shape? I was wondering when in history did people start use the $\sqrt{}$ sign for square root, what did they use before, and why this curious nomenclature is adopted.
 A: You can find information about the history of the usage in Jeff Miller's page here: Earliest Uses of Symbols of Operation.
Quoted:

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
  90).
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).

A: The correct answer is that the Arabic letter jeem ج which is the first letter in the Arabic Jathr جذر meaning root, Algebra on the other hand was invented by a muslim scholar which is Arabic word for al-jabr "restoration"  
