An Exponents & Radicals Investigation has been added to the Highlights section of Exponents and Radicals.

Students struggle filling out the table on the first page so I usually do that with them to establish the two different ways to express the side length.  Then they can use that information as well as the "If these are true ..." examples on the next page to see if they can figure out how to change entire radicals to mixed radicals.  I find the key to these investigations is to not give in and tell them the answer.  I usually like to have an assignment or an exit slip ready to go so that those that understand the concept can move onto the assignment after they show me they understand. Some students may require some hints and I find that the ones that get it will often help out classmates that don't.  I hope it works well for you if you try it.

Colin