Discover solutions of radical equations and investigate extraneous solutions.

• Students will determine the solution of radical equations both algebraically and geometrically.
• Students will know why solutions to radical equations should be checked by algebraic solution for extraneous solutions.
• Students will establish the relationship between real and nonreal number solutions for radical equations.
• Students will be able to explain why squaring both sides of an equation can lead to extraneous solutions.

• radical equations
• real numbers
• extraneous solutions

This lesson allows students to discover solutions of radical equations and investigate extraneous solutions. As a result, students will:

• Solve radical equations using handheld graphing technology.
• Solve radical equations using algebra and test the validity of the solution.
• Justify the solution(s) of a radical equation.