Find principal roots

Find principal roots


If n is even, positive numbers have two nth roots.For example, both 4 and -4 are square roots of 16, and 2 and -2 are fourth roots of 16. In such cases, the notation \sqrt[n]{a} represents the positive root, called the principal root.


nth Root

If n is even and a is positive or 0, then

\sqrt[n]{a} represents the principal nth root of a, and

\sqrt[n]{a} represents the negative nth root of a.

If n is even and a is negative, then

\sqrt[n]{a} is not a real number.

If n is odd, then

there is exactly one nth root of a, written \sqrt[n]{a}


If n is even, then the two nth roots of a are often written together as

\pm  \sqrt[n]{a} ,with \pm  read “positive or negative.”.


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