8 8 Solving Radical Equations and Inequalities Objective

8 -8 Solving Radical Equations and Inequalities Objective Solve radical equations and inequalities. SOLVING RADICAL EQUATIONS: #1: _______ the _______ #2: Raise both sides to the _____ of the ____. Example 1: Solving Equations Containing One Radical Solve each equation. Check your answer on your calculator. A. C. B.

8 -8 Solving Radical Equations and Inequalities Example 2: Solving Equations Containing Two Radicals Solve and check your answer on your calculator. A. B. C.

8 -8 Solving Radical Equations and Inequalities Raising each side of an equation to an even power may introduce _______ solutions. Example 3: Solving Equations with Extraneous Solutions A. Solve Method 1 Use a graphing calculator. B. Method 2 Use algebra to solve the equation. Solve the equation. Method 1 Use a graphing calculator. Method 2 Use algebra to solve the equation.

8 -8 C. Solving Radical Equations and Inequalities Solve. Example 4: Solving Equations with Rational Exponents Solve each equation. 1 A. (5 x + 7) 3 = 3 1 C. (x + 5) 3 =3 B. 2 x = (4 x + 8) 1 2

8 -8 Solving Radical Equations and Inequalities Example 5: Solving Radical Inequalities A. Solve. . Method 1 Use a graph and a table. Method 2 Use algebra to solve the inequality. B. Solve. Method 1 Use a graph and a table. Method 2 Use algebra to solve the inequality. Example 6: Application The speed s in miles per hour that a car is traveling when it goes into a skid can be estimated by using the formula s = 30 fd, where f is the coefficient of friction and d is the length of the skid marks in feet. A car skids to a stop on a street with a speed limit of 30 mi/h. The skid marks measure 35 ft, and the coefficient of friction was 0. 7. Was the car speeding? Explain.