Drill #63 Find the following roots: Factor the following polynomial:

Drill #64 Find the following roots:

Drill #65 Find the following roots:

Drill #66 Simplify each expression:

Drill #70 Simplify each expression:

5-6 Radical Expressions Objective: To simplify radical expressions, to rationalize the denominator of radical expressions, and to add, subtract, multiply and divide radical expressions.

(1.) Product Property of Radicals ** Definition: For any real numbers a and b, and any integer n, n > 1, Example:

Examples/Classwork* Example: Example 1 (5-6 Study Guide) 5-6 Study Guide #1 – 3

(2.) Quotient Property of Radicals ** Definition: For real numbers a and b, b = 0, and any integer n, n > 1, Example:

Simplifying Radical Expressions: Using the Product Property Simplify the following:

Examples: 5-6 Skills Practice #5,6

Simplifying Radical Expressions: Using the Quotient Property Simplify the following:

(3.)Rationalizing the Denominator ** Definition: To rationalize the denominator you must multiply the numerator and denominator by a quantity so that the radicand (what’s inside the radical) has an exact root. We rationalize the denominator so that there are no radicals in denominator.

Rationalizing the Denominator* Example: 5-6 Study Guide

(4.) Like Radical Expressions Definition: Two radical expressions that have the same indices and the same radicand. To simplify like radical expressions add (or subtract) the coefficients. Examples:

Like Radical Expressions Group together all like radical expressions

Like Radical Expressions Group together all like radical expressions

Adding and Subtracting Radical Expressions* To add and subtract radical expressions: 1. Simplify all radicals in the expression to simplest form 2. Group together all like terms (non-radicals and radicals) 3. Add/subtract like terms to simplify Example:

Adding and Subtracting Radical Expressions* To add and subtract radical expressions: 1. Simplify all radicals in the expression to simplest form 2. Group together all like terms (non-radicals and radicals) 3. Add/subtract like terms to simplify Example:

Adding and Subtracting Radical Expression* To add and subtract radical expressions: 1. Simplify all radicals in the expression to simplest form 2. Group together all like terms (non-radicals and radicals) 3. Add/subtract like terms to simplify Example:

Multiplying Radical Expressions* To multiply radical expressions: 1. Use the distributive property (or FOIL) to multiply 2. Use the product property to multiply radicals. 3. Simplify each radical expression. 4. Combine like terms Example:

Multiplying Radical Expressions* Examples:

(5.) Conjugates** Definition: The conjugate of a radical expression is formed by changing the sign of the operation that joins the terms. Radical ExpressionConjugate

Multiplying conjugates What happens when you multiply conjugates?

Rationalize Radical Denominators* To rationalize radical denominators, multiply the numerator and the denominator by the conjugate of the denominator.

Rationalize Denominators* Examples: 5-6 Study Guide, Example 3

Drill #70 (Multiply Radicals) Simplify each expression:

Drill #70 (Divide Radicals) Simplify each expression:

Drill #70 (Add Radicals) Simplify each expression:

Drill #70 (Multiply Complex Radicals) Simplify each expression:

Drill #70 (Divide Complex Radicals) Simplify each expression:

Drill #70 (Divide Complex Radicals) Simplify each expression: