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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.

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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 alt text (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 alt text, adding the vinculum to the radical symbol La Geometrie (Cajori vol. 1, page 375).

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Cajori should always be everybody's first stop when looking for notation history. –  J. M. Dec 29 '10 at 1:47
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If you're not looking for crazy amounts of information, there's always this!

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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"

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