This activity is designed to be used for groups of 4, 3 and/or 2 members. It practices:
• solving radical equations with one and two square roots
• solving linear and quadratic equations
• checking for extraneous solutions
The radical equations contain:
* a monomial and/or a binomial under a radical symbol
* a radical expression on one side of the equation and a monomial or a binomial on the other side
*radical expressions on one side and respectively on the both sides of the equations (“radical equals radical”)
Most of the equations require rearranging and isolating the radical and the rest are set up to square both sides. All the equations require squaring once.
Activity Directions: Partners will each have their own set of eight problems of various difficulty. They reduce them to linear or quadratics and continue solving by any method they choose. Students write down the solutions of the problems on the recording sheet provided. They are instructed to check for extraneous solutions.
Partners record their answers in tables on a group response sheet designed in such a way that students can analyze and compare their results easily. They must verify that all equations actually have the same solution except only one which has two distinct roots. I called this special equation “black sheep equation” and it is the equation B8. It can not be simply found without checking for extraneous solutions.
All answer keys are provided. I hope your students enjoy searching for the “black sheep” and have fun with this activity.
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