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