Extraneous solutions to radical equations

The  exercise appears under the Algebra I Math Mission. This exercise helps cultivate understanding of extraneous solutions as opposed to actual solutions (and non-solutions).

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


 * 1) Select the type of solution: This problem has an exercise and several possible solutions to the equation. The student is asked to select whether each value is an actual solution, an extraneous solution, or not a solution.Estre1.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.