nth Root - Identities and Properties

Identities and Properties

Every positive real number has a positive nth root and the rules for operations with such surds are straightforward:

Using the exponent form as in normally makes it easier to cancel out powers and roots.

Problems can occur when taking the nth roots of negative or complex numbers. For instance:

whereas

when taking the principal value of the roots. See failure of power and logarithm identities in the exponentiation article for more details.