We'll include this section with the definition of the radical.  If n is a +ve integer that is greater than one and a is a real number then,

Where n is termed as the index, a is said to be the radicand, and the symbol  √       is called the radical. The left side of this equation is frequently called the radical form & the right side is frequently called the exponent form.

From this definition we can notice that a radical is just another notation for the first rational exponent .

Notice as well that the index is needed in these to ensure that we properly evaluate the radical. There is one exception to this rule & that is square root.  For square roots we have,

In other terms, for square roots typically we drop the index.

Let's do example to understand this new notation.