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}](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-caef3fd00aded6261ac76277958994d0_l3.png "Rendered by QuickLaTeX.com")
represents the positive root, called the principal root.
nth Root
If n is even and a is positive or 0, then
represents the principal nth root of a, and
– represents the negative nth root of a.
If n is even and a is negative, then
is not a real number.
If n is odd, then
there is exactly one nth root of a, written
If n is even, then the two nth roots of a are often written together as
,with read “positive or negative.”.