Example 2 — Simplify: Step 1: Find the prime factorization of the number inside the radical and factor each variable inside the radical.
In this example, the largest factor that both numbers have in common is 2. But there are other ways in which a fraction can become complicated. To simplify radicals, rather than looking for perfect squares or perfect cubes within a number or a variable the way it is shown in most books, I choose to do the problems a different way, and here is how.
Or, to put it another way, you'll get the same result if you flip that second fraction upside down creating the inverse and multiply by that, which is a much easier operation to perform.
For example, if the index is 2 a square rootthen you need two of a kind to move from inside the radical to outside the radical. If the index is 3 a cube rootthen you need three of a kind to move from inside the radical to outside the radical.
Simplifying Complex Fractions Another common obstacle you might encounter to writing a fraction in its simplest form is a complex fraction — that is, a fraction that has another fraction in either its numerator or its denominator, or both. Step 2: Determine the index of the radical.