# Holt McDougal Algebra 2 5-8 Solving Radical Equations and Inequalities Warm Up Simplify each expression. Assume all variables are positive. Write each.

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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.

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.

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

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

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

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

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

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

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!

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

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

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