1. 1 7.5 Solving Radical Equations

2. 2 What is a radical equation? A radical equation is an equation that has a variable under a radical or that has a variable with a fractional exponent. Examples: This is a radical equation. This is not a radical equation. (It is a linear equation)

3. 3 Solve the radical equation

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10. 10 Solve the radical equation

11. 11 Solve the radical equation

12. 12 Sometimes there is more than one variable in the problem… Square both sides to eliminate the radical Here is a graph of the problem:

13. 13 Sometimes there is more than one variable in the problem… Square both sides to eliminate the radical Here is a graph of the problem: This graph only shows a solution at x = 7. This is called an extraneous solution.

14. 14 Extraneous Solutions An extraneous solution is a solution that emerges from the process of solving the problem using correct Algebra steps but is not a valid solution to the original problem. Example: Square both sides Take the square root of bodes sides Where did the solution x = -1 come from? It clearly does not fit the original equation. Certain operations can generate extraneous solutions. The list of these operations include: a.) Square both sides b.) Multiply by a variable

15. 15 Here are the possible graphs of solutions to an equation involving a square root. The equation has 2 correct solutions. The equation has 1 correct solution. The equation has 0 correct solutions.

16. 16 Here are the possible graphs of solutions to an equation involving a square root. The equation has 1 correct solution and 1 extraneous solution. The equation has 2 extraneous solutions.

17. 17 Solve the equation. Check for extraneous solutions.

18. 18 Solve the equation. Check for extraneous solutions. Extraneous

19. 19 Solve the equation. Check for extraneous solutions. Extraneous

20. 20 Solve the equation. Check for extraneous solutions. Not factorable. Use the Quadratic formula Extraneous

21. 21 Solve the equation. Check for extraneous solutions.

22. 22 Solve the equation. Check for extraneous solutions. extraneous