Radical

The symbol  used to indicate a root is called a radical, or sometimes a surd. The expression  is therefore read " radical ," or "the nth root of ." In the radical symbol, the horizonal line is called the vinculum, the quantity under the vinculum is called the radicand, and the quantity  written to the left is called the index.

In general, the use of roots is equivalent to the use of fractional exponents as indicated by the identity

(1)

a more generalized form of the standard

(2)

The special case  is written  and is called the square root of .  is called the cube root.

Some interesting radical identities are due to Ramanujan, and include the equivalent forms

(3)

and

(4)

Another such identity is

(5)

REFERENCES:

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1168, 2002.