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Principal Root

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Principal Root

If a number raised to the power gives it is said that is an root of
In many cases, some numbers have more than one real root. For example, has two square roots, and
In this case, the principal root of is the positive root since it has the same sign as In general, the principal root of a number is the root that has the same sign as It is denoted by the radical symbol and is the index of the radical.

A special case is when is and odd number and is negative. In this situation, there will be no nonnegative root and the principal root is negative. Some examples of roots and its description can be seen below.

root Description
indicates the principal square root of
indicates the opposite of the principal square root of
indicates both square roots of
indicates the principal cube root of
indicates the principal fifth root of
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