Radical

A radical, sometimes called a surd, is the symbol used to indicate a nth root. The expression is therefore read " radical ," or "the nth root of ." In the radical symbol, the horizontal 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.

For , a positive integer , and an integer , roots are equivalent to fractional exponents as indicated by the identity

(1)

which generalizes, for and a positive integer , the standard identity

(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 (Berndt et al. 1998, p. 146) and include the equivalent forms

(3)

and

(4)

Another such identity is

(5)