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A surd is a number or quantity that cannot be expressed as the ratio of two integer s. The term also refers to a symbol ( ) that is sometimes used to indicate that the number or quantity that follows it is a root.

The surd symbol, all by itself, indicates the square root (1/2 power). If the surd has a number x written ahead of it and over the horizontal portion, then the symbol refers to the x th root (1/ x power) of that number. Therefore, for example:

indicates the cube root (1/3 power)

indicates the fourth root (1/4 power)

indicates the -7th root (-1/7 power)

indicates the n th root (1/ n power)

The extent of the quantity affected by the surd, and that follows it, is indicated by placing a horizontal line over that quantity. The most common example is the square root symbol .

Also see Mathematical Symbols .

This was last updated in September 2005

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