Analyze extraneous solutions of radical equations

The  exercise appears under the Algebra II Math Mission. This exercise practices some problems that involve thinking about the conditions for obtaining extraneous solutions while solving radical equations.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the value that makes the constant an extraneous solution: This problem has a radical equation that involves variables. The student is asked find the value that makes the constant an extraneous solution and type it in the text box below. Analyze extraneous solutions of radical equations.PNG

Strategies
An ability to solve an equation, and to check answers by plugging the solution back into the equation, are both needed to ensure success on this exercise.
 * 1) Rather than solving the equation, it can be more efficient to plug in the answer choices without solving.
 * 2) When plugging in, if both sides of the equation are the same value then it is an actual solution.
 * 3) When plugging in, if both sides of the equation are the same number but have opposite signs, then it is an extraneous solution. The process of squaring made the two sides the same extraneously.
 * 4) When plugging in, if both sides of the equation are different values then it is not a solution.

Real-life Applications

 * 1) Solving equations is an important skill in all classes beyond algebra.
 * 2) Radical equations occur when using approximations to find the height of a mountain using the curvature of the earth.