"Closure of Root Three Numbers," like many other problems you’ll find here, isn’t a single problem. It is a problem sequence, in this case containing 14 problems divided into 3 parts. These 14 problems are not separate. They are carefully organized to let students explore the idea of closure. At the same time, this sequence provides students with an ample opportunity to practice binomial multiplication involving radicals. These exercises do not feel repetitious, because every step in this sequence has a purpose besides simple manipulation.

Every problem sequence has a problem statement and answers; most also have hints and solutions. All of them were written to be educational for students. At the same time, solutions can include teacher notes in the margins, with suggestions for teachers about the ways to use the problems. Please take time to look at all parts of the problem.

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