Holt McDougal Algebra 2
5-8 Solving Radical Equationsand Inequalities
Warm UpSimplify 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 Equationsand Inequalities
Solve radical equations and inequalities.
Objective
Vocabulary
radical equationradical inequality
Holt McDougal Algebra 2
5-8 Solving Radical Equationsand 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 Equationsand Inequalities
Solve each equation.
Example 1: Solving Equations Containing One Radical
Holt McDougal Algebra 2
5-8 Solving Radical Equationsand Inequalities
Example 2: Solving Equations Containing Two Radicals
Solve
Holt McDougal Algebra 2
5-8 Solving Radical Equationsand 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 Equationsand Inequalities
Example 3
Use algebra to solve the equation.
Holt McDougal Algebra 2
5-8 Solving Radical Equationsand Inequalities
Solve with a table and graph.
Example 3: Solving Equations with Extraneous Solutions
Holt McDougal Algebra 2
5-8 Solving Radical Equationsand Inequalities
Example 4: Solving Equations with Rational Exponents
Solve each equation.
(5x + 7) = 313 2x = (4x + 8)
12
Holt McDougal Algebra 2
5-8 Solving Radical Equationsand 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 Equationsand Inequalities Example 5: Solving Radical Inequalities
Method 2 Use a graph and a table.
Solve agebraically
Holt McDougal Algebra 2
5-8 Solving Radical Equationsand Inequalities
Example 6: Automobile Application
Pages 381-383 #27-49, 51, 58, 59, 60, 62-65