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.
Read more about this topic: nth Root
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“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)