Explain how you know if a radical expression is in simplest form
A radical expression is in its simplest form when the radicand (the number under the radical symbol) is not a perfect square, and there are no perfect square factors in the radicand that can be simplified further.
To determine if a radical expression is in simplest form, you should check if the radicand can be simplified by factoring out perfect square factors. If there are no perfect square factors that can be simplified, then the radical expression is in its simplest form.
For example, the radical expression √12 can be simplified because 12 can be factored as 4 x 3, where 4 is a perfect square. Therefore, √12 = 2√3, which is in its simplest form. On the other hand, the radical expression √15 cannot be simplified further, as 15 does not have any perfect square factors other than 1, so it is already in its simplest form.