Radical expressions

In this discussion you will reflect on your knowledge of radical expressions.

Instructions:

1. Post a response to the following questions:
   1. Why is it important to simplify radical expressions before adding or subtracting?
   2. Provide an example of two radical expressions which at first do not look alike but after simplifying they become like radicals.

Answer preview

Similarly, radical terms cannot be combined unless the value under the radical is the same for both terms. One can discover whether radical phrases are similar and can be merged by first simplifying the radical terms. Only radical expressions with the same index and radicand can be added to or subtracted. There cannot be any elements in a simplified radical that are perfect squares under the radical. The only way to get rid of them is to factor them out of the radicand, calculate their square root, and then use the resulting value as a coefficient. The denominator is rationalized to eliminate the simplified radical, which cannot have any radicals in it . The first and last terms are “like” terms. Both are numbers multiplied by  √2, which can be simplified and subtracted. The like terms can be added or subtracted to give 9√2. Another example is , where the radical expression can be simplified into.

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