1. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Warm Up Simplify each expression. Assume all variables are positive. Write each expression in radical form. 1. 2. 3. 4. 5. 6.

2. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Solve radical equations and inequalities. Objective Vocabulary radical equation radical inequality

3. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities A radical equation contains a variable within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a power.

4. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Solve each equation. Example 1: Solving Equations Containing One Radical

5. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Example 2: Solving Equations Containing Two Radicals Solve

6. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Raising each side of an equation to an even power may introduce extraneous solutions. You can use the intersect feature on a graphing calculator to find the point where the two curves intersect. Helpful Hint

7. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Example 3 Use algebra to solve the equation.

8. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Solve with a table and graph. Example 3: Solving Equations with Extraneous Solutions

9. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Example 4: Solving Equations with Rational Exponents Solve each equation. (5x + 7) = 3 1 3 2x = (4x + 8) 1 2

10. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities A radical inequality is an inequality that contains a variable within a radical. You can solve radical inequalities by graphing or using algebra. A radical expression with an even index and a negative radicand has no real roots. Remember!

11. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Example 5: Solving Radical Inequalities Method 2 Use a graph and a table. Solve agebraically

12. Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Example 6: Automobile Application Pages 381-383 #27-49, 51, 58, 59, 60, 62-65