Drill #75: Simplify each expression

Drill #76: Solve each equation

Drill #77: Solve each equation

(1.) Radical Equations** Definition: Equations that contain radical expressions. To solve equations that contain radical expressions: 1. Isolate the radical 2.Raise each side of the equation to the power of the index. (use the reciprocal for fractional powers. 3.Repeat until all roots have been eliminated. 4.Solve the equation. (using S.G.I.R.)

Solving Equations with Radical Coefficients 1. Group the variables and constants on opposite sides 2. Factor the variable 3. Divide by the coefficient (the parenthesis 4. Rationalize the denominator

Radical Exponents Example 1:

Solving Radical Equations* (when the variable is under the radical) 1. Isolate the radical (on one side of the equation) NOTE: If there are more than one radical isolate one radical at a time. 2.Eliminate the radical (by raising each side of the equation to a power equal to the index of the radical) REPEAT THIS STEP UNTIL ALL Radicals have been eliminated 3. Solve the equation 4. Check your solution!!! (some solutions may not work)

Examples* One Radical: Ex1: 5-8 Study Guide PI: Example 1 Ex2: 5-8 Study Guide PII: Example 1 Multiple Radicals: Ex3: 5-8 Study Guide PI: Example 2 Ex4: 5-8 Study Guide PII: Example 2

(2.) Extraneous Solutions** Definition: Solutions that do not satisfy the original equation. NOTE: Squaring the equation can create solutions that do not work in the original equation. Example:

(3.) Zero Product Property** Definition: If the product of two numbers a(b) = 0 then either a = 0 or b = 0 or both Example: x(x – 1) = 0 x = 0 or x – 1 = 0 x = 1

4 Types of Radical Equations* Radical Coefficient:S.G.I.R. Variable under the Radical: 1 radical Variable under the Radical: 2 radicals (no const.) Variable under the Radical: 2 radicals (w/ const.)

Using the zero-product property* Examples: 5-8 Study Guide: Extraneous Solutions #1, #2, #6

Nth Roots*

Solving Radical Inequalities* Steps for solving radical inequalities: 1.Radicand must be positive If the index of the radical is even (square root, fourth root, etc.) identify values of the variable which will make the radicand positive (SPECIAL CASE) 2. Solve the inequality (set up a compound inequality joining the solutions from 1. and 2.) 3. Check solution. Test values (one less, one in the middle, one greater) to make sure the solution works

Solving Radical Inequalities* Ex 1: 5-8 Study Guide: Solve Radical Inequalities, Example 1