I take no credit for this idea at all. I was in a classroom this morning, and the teacher had the students play a game of Radical SNAP. The students were totally engaged, and were enthusiastically converting between mixed and entire radicals. It’s pretty simple to set up.
Materials: You need one deck of cards with the 10, J, Q and K removed for each pair of students, and one giant square root symbol per pair of students. This one should do the trick: Giant Root
Pair off the students in your class. Each pair gets a deck of cards, and should remove the 10, J, Q and K. Shuffle the remaining cards, and deal them so that each person has half the deck, face down.
Mixed to Entire
The students flip over their top cards. The student on the left puts his in front of the radical, and the student on the right puts hers under the radical. The first student to correctly convert the mixed radical to an entire radical wins the round.
Entire to Mixed
The students flip over their top cards, and put them both under the radical. The first student to correctly simplify the radical or to identify that it can’t be simplified wins the round.