If we "break up" the root into the total of two pieces clearly we get different answers.

Simplified radical form:

We will simplify radicals shortly so we have to next define simplified radical form.  A radical is called to be in simplified radical form (or simplified form) if each of the following are true.

1.   All exponents in the radicand have to be less than the index.

2.  In the radicand any exponents can have no factors in common along the index.

3.   No fractions seem under a radical.

4.   No radicals seem in the denominator of a fraction.