Download presentation

Presentation is loading. Please wait.

Published byLionel Marsh Modified over 7 years ago

1
Drill #63 Find the following roots: Factor the following polynomial:

2
Drill #64 Find the following roots:

3
Drill #65 Find the following roots:

4
Drill #66 Simplify each expression:

5
Drill #70 Simplify each expression:

6
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.

7
(1.) Product Property of Radicals ** Definition: For any real numbers a and b, and any integer n, n > 1, Example:

8
Examples/Classwork* Example: Example 1 (5-6 Study Guide) 5-6 Study Guide #1 – 3

9
(2.) Quotient Property of Radicals ** Definition: For real numbers a and b, b = 0, and any integer n, n > 1, Example:

10
Simplifying Radical Expressions: Using the Product Property Simplify the following:

11
Examples: 5-6 Skills Practice #5,6

12
Simplifying Radical Expressions: Using the Quotient Property Simplify the following:

13
(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.

14
Rationalizing the Denominator* Example: 5-6 Study Guide

15
(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:

16
Like Radical Expressions Group together all like radical expressions

17
Like Radical Expressions Group together all like radical expressions

18
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:

19
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:

20
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:

21
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:

22
Multiplying Radical Expressions* Examples:

23
(5.) Conjugates** Definition: The conjugate of a radical expression is formed by changing the sign of the operation that joins the terms. Radical ExpressionConjugate

24
Multiplying conjugates What happens when you multiply conjugates?

25
Rationalize Radical Denominators* To rationalize radical denominators, multiply the numerator and the denominator by the conjugate of the denominator.

26
Rationalize Denominators* Examples: 5-6 Study Guide, Example 3

27
Drill #70 (Multiply Radicals) Simplify each expression:

28
Drill #70 (Divide Radicals) Simplify each expression:

29
Drill #70 (Add Radicals) Simplify each expression:

30
Drill #70 (Multiply Complex Radicals) Simplify each expression:

31
Drill #70 (Divide Complex Radicals) Simplify each expression:

32
Drill #70 (Divide Complex Radicals) Simplify each expression:

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google