Explain how you know if a radical expression is in simplest form.
A radical expression is in simplest form when the radicand (the number or expression inside the radical) has been simplified as much as possible and the index (the small number outside the radical) cannot be reduced further.
To determine if a radical expression is in simplest form, follow these steps:
1. Simplify the radicand by factoring out perfect square factors, reducing fractions, or simplifying any other expressions inside the radical.
2. Check if the index can be reduced. The index represents the root being taken, such as square root (index 2), cube root (index 3), etc. If the index can be reduced, then do so by finding a lower perfect power of the radicand.
3. Remove any unnecessary square roots, such as converting a square root to its rational form. For example, if the radicand is a perfect square, you can convert it to the square of an integer.
4. Confirm that there are no common factors between the radicand and the index. If there are, divide the radicand and the index by their greatest common factor.
If after following these steps, there are no more simplifications possible, then the radical expression is in its simplest form.