It is important to have a basic grasp of the concept of simplifying radicals before beginning any games with them. A radical is any number presented in square root form. For example, √33, √12, and √72 are all radicals. A simplified radical is a number that no longer has square factors. For example, √33 is already in its simplest form. The equation 3x11 is used to produce 33, and neither 3 nor 11 is a square number. However, √12 is not in its simplest form. For any problem, there is a theorem to help solve radicals. This theorem is: √ab = √a x √b. Using this theorem, √12 is broken down to √3x4. Since the square root of 4 is 2, the final equation becomes 2√3.
For a trouble-free way to start simplifying radicals, "Cool Math" has an application that brings up radical problems to solve and allows you to check your answer in a space below. Sometimes, if you are having difficulty getting started, it can help to reveal the answer from the beginning and work backwards to discover what steps must be done to get the correct simplified form. As you start to become comfortable with the concepts, test yourself. How many correct problems can you get in a row? How many radicals can you simplify in 5 minutes? You can even go head to head with a teammate and challenge each other to a duel to see who can get the most correct answers in a predetermined time period.
Quia.com is a site that allows educators, students, and other users to post quizzes and games for just about any topic you can think of, including simplifying radicals. From the home page, click the "Go" button in the "Shared Activities" section. This will open a search engine field. Type in "simplifying radicals." This will bring up quizzes and games to help study the concept.
Use card games to teach students the concept of sorting and simplifying radicals. Hand out a deck of cards to groups of 3 to 4 students. Have each group select a dealer who hands out 10 to 15 cards to each student. Students look at their cards face up and are instructed to sort them. Each student picks out sets of two cards that have the same number or face value and sets these to the side. Repeat the activity making sets of three-of-a-kinds and four-of-a-kinds. Tell the students to sorting their cards into "books." Write an equation on the board, for example: √25 x A^4 x B^3. Extend the radical, writing √5 x 5 x A x A x A x A x B x B x B. Just like with the cards, ask students to find three-of-a-kinds, which in the case of the extended radical includes three of the "A"s and the three "B"s. The "books" are placed to the left of the equation, while anything extra is kept to the right, like this: A x B √5 x 5 x A. Now, students simplify the numbers left to the right: A x B √25 x A. This particular equation can be further simplified to: A x B x 5 √A. This game makes a difficult looking equation become much more approachable.