1. Exploring Polynomials and Radical Expressions Advanced Algebra Chapter 5

2.  Basic steps for solving equations with radicals.  For example: 1.Square Both Sides  2.Simplify Each Side  3.Solve The Equation  Method 1 for Solving Equations with Radicals Using the Quadratic Formula

3.  Basic steps for solving equations with radicals.  For example: 1.Variables to One Side  2.Factor Out Variable  3.Isolate Variable  Method 2 for Solving Equations with Radicals

4.  Solve the following eqaution. Practice for Solving Equations with Radicals

5.  Activity  Measure your desktops  length (l), width (w) and diagonal (d).  Use the Pythagorean Theorem to check the measurements.  d 2 = l 2 + w 2   Why do we discard the negative value?  This is known as an extraneous solution. Application of Equations with Radicals

6.  An extraneous solutions are solutions which do not satisfy the original equation. Check All Solutions!!  Therefore you must Check All Solutions!!  In a previous example we had the equation  The solution was  After checking, solution is now Application of Equations with Radicals

7.  For example: 1.Identify excluded values. Radicand of the radical must be greater than 0. 2.Now solve the inequality. 3.Test values on a number line to find the solution. Method for Solving Inequalities with Radicals -2012453-36789 Try y = 0Try y = 1Try y = 6 False  y = 0, yields a negative square root. True  y = 1, yields 1  3. Solution: False  y = 6, yields

8.  Solve the following radical equations. 1. 2. Practice for Solving Inequalities with Radicals