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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The $n_{th}$ root of a number $a$ expresses another number that, when multiplied by itself $n$ times, will result in $a.$ Aside from the radical symbol, the notation is made up of the radicand $a$ and the index $n.$

The resulting number is commonly called a **radical**. For example, the radical expression $416 $ is the fourth root

of $16.$ $416 $ simplifies to $2$ because $2$ multiplied by itself $4$ times equals $16.$
$416 =42_{4} =2 $
The general expression $na $ represents a number which equals $a$ when multiplied by itself $n$ times.

$ntimesna ⋅na ⋅…⋅na =aor(na )_{n}=a$

The $n_{th}$ root can also be expressed using a rational exponent.

$na_{1} =a_{n1}$

Just as with exponents, the most common roots have special names: square roots and cube roots have an index of $2$ and $3,$ respectively.