### Never, Ever Simplify

Today in calculus I taught the chain rule. We started class with some warm-up problems based on what we'd been learning before. At the end of the warm-ups, I had some algebra questions.

First I asked if the following expression was equal to

The vast majority of the students said that yes it was. (That's the great thing about having the clickers; as soon as the question ends, a bar graph of the responses appears on my screen.) I explained that it didn't simplify like that.

Then I asked whether this expression equals

Again, most of the students answered yes.

At this point I told them that for the rest of the semester that they should assume that radicals never simplify.

First I asked if the following expression was equal to

*x*^{2}+*x*.The vast majority of the students said that yes it was. (That's the great thing about having the clickers; as soon as the question ends, a bar graph of the responses appears on my screen.) I explained that it didn't simplify like that.

Then I asked whether this expression equals

*x*+ 2.Again, most of the students answered yes.

At this point I told them that for the rest of the semester that they should assume that radicals never simplify.