How you know if a radical expression is in simplest form.
To determine if a radical expression is in simplest form, you should check if the radicand (the number under the radical symbol) has any factors that can be further simplified.
Here are the steps to determine if a radical expression is in simplest form:
1. Look at the radicand.
2. Check if the radicand has any perfect square factors. A perfect square factor is a number that can be multiplied by itself to give the radicand. For example, in the expression √12, the radicand is 12, and its perfect square factors are 1, 4, and 9.
3. If you find any perfect square factors, simplify them. For example, if the radicand is 12 and you find the perfect square factor 4, you can simplify it by taking the square root of 4, which is 2. This would result in √12 = 2√3.
4. Repeat steps 2 and 3 until there are no more perfect square factors in the radicand.
5. If there are no more perfect square factors in the radicand, the radical expression is in its simplest form.
Note: It's important to simplify the expression as much as possible, but if the radicand cannot be further simplified (i.e., if it does not have any perfect square factors), then the radical expression is already in its simplest form.