If a number $b$ raised to the $n^{\text{th}}$ power gives $a,$ it is said that $b$ is an $n^{\text{th}}$ root of $a.$ In many cases, some numbers have more than one real $n^{\text{th}}$ root. For example, $9$ has two square roots, $3$ and $\text{-}3.$ In this case, the principal root of $9$ is the positive root $3,$ since it has the same sign as $9.$ In general, the principal $n^{\text{th}}$ root of a number $a$ is the $n^{\text{th}}$ root that has the same sign as $a.$ It is denoted by the radical symbol and $n$ is the index of the radical.

A special case is when $n$ is and odd number and $b$ is negative. In this situation, there will be no nonnegative root and the principal root is negative. Some examples of $n^{\text{th}}$ roots and its description can be seen below.

$n^{\text{th}}$ root	Description
$\sqrt{16}=4$	$\sqrt{16}$ indicates the principal square root of $16.$
$\text{-}\sqrt{16}=\text{-}4$	$\text{-}\sqrt{16}$ indicates the opposite of the principal square root of $16.$
$\pm \sqrt{16}=\pm 4$	$\pm \sqrt{16}$ indicates both square roots of $16.$
$\sqrt[3]{\text{-}125}=\text{-}5$	$\sqrt[3]{\text{-}125}$ indicates the principal cube root of $\text{-}125.$
$\sqrt[5]{\text{-}243}=\text{-}3$	$\sqrt[5]{\text{-}243}$ indicates the principal fifth root of $\text{-}243.$