1. Tomorrow I want start my date, to put everything in order and check my class and my new lesson an also reflect about my life my future

2. Copyright © 2007 Pearson Education, Inc. Slide R-2 R.8 nth Roots and Rational Expressions: Simplify Expressions with Rational Exponents Simplifying Expressions Containing Rational Exponents: Recall the following from Review Section 2: Laws of Exponents: For any integers m, n (assuming no divisions by 0) new! and

3. Copyright © 2007 Pearson Education, Inc. Slide R-3 R.8 nth Roots and Rational Expressions In this section, we will… Evaluate nth Roots Simplify Radical Expressions Add, Subtract, Multiply and Divide Radical Expressions Rationalize Denominators Simplify Expressions with Rational Exponents Factor Expressions with Radicals or Rational Exponents Chapter R Section 1: nth Roots and Rational Exponents

4. Copyright © 2007 Pearson Education, Inc. Slide R-4 R.5 Review of Radicals In the expression is called a radical sign, a is called the radicand, n is called the index. Remember that the index, n, is a whole number equal to or greater than 2.

5. Copyright © 2007 Pearson Education, Inc. Slide R-5 R.5 Review of Radicals Radical Notation for a 1/n If a is a real number, n is a positive integer, and a 1/n is a real number, then

6. Copyright © 2007 Pearson Education, Inc. Slide R-6 Radical Rational Exponents Examples:

7. Copyright © 2007 Pearson Education, Inc. Slide R-7 R.5 Review of Radicals Evaluating If n is an even positive integer, then If n is an odd positive integer, then Negative numbers do not have real # square roots The principal root of a positive number is positive

8. Copyright © 2007 Pearson Education, Inc. Slide R-8 R.5 Evaluating Roots Example Evaluate each root. (a) (b)(c) Solution (a) (b) is not a real number. (c)

9. Copyright © 2007 Pearson Education, Inc. Slide R-9 R.5 Review of Radicals Radical Notation for a m/n If a is a real number, m is an integer, n is a positive integer, and is a real number, then

10. Copyright © 2007 Pearson Education, Inc. Slide R-10 R.5 Converting from Rational Exponents to Radicals Example Write in radical form and simplify. (a) (b)(c) Solution (a) (b) (c)

11. Copyright © 2007 Pearson Education, Inc. Slide R-11 R.5 Converting from Radicals to Rational Exponents Example Write in exponential form. (a) (b)(c) Solution (a)(b) (c)

12. Copyright © 2007 Pearson Education, Inc. Slide R-12 R.5 Using Absolute Value to Simplify Roots Example Simplify each expression. (a) (b)(c) Solution (a) (b) (c)

13. Copyright © 2007 Pearson Education, Inc. Slide R-13 R.5 Review of Radicals Rules for Radicals For all real numbers a and b, and positive integers m and n for which the indicated roots are real numbers,

14. Copyright © 2007 Pearson Education, Inc. Slide R-14 R.5 Using the Rules for Radicals to Simplify Radical Expressions Example Simplify each expression. (a) (b)(c) Solution (a) (b) (c)

15. Copyright © 2007 Pearson Education, Inc. Slide R-15 R.5 Simplifying Radicals Simplified Radicals An expression with radicals is simplified when the following conditions are satisfied. 1. The radicand has no factor raised to a power greater than or equal to the index. 2. The radicand has no fractions. 3. No denominator contains a radical. 4. Exponents in the radicand and the index of the radical have no common factor. 5. All indicated operations have been performed (if possible).

16. Copyright © 2007 Pearson Education, Inc. Slide R-16 R.5 Simplifying Radicals Example Simplify each radical. (a) (b) Solution (a) (b)

17. Copyright © 2007 Pearson Education, Inc. Slide R-17 R.5 Simplifying Radicals by Writing Them with Rational Exponents Example Simplify each radical. (a) (b) Solution (a) (b)

18. Copyright © 2007 Pearson Education, Inc. Slide R-18 R.5 Adding and Subtracting Like Radicals Example Add or subtract, as indicated. Assume all variables represent positive real numbers. (a) (b) Solution (a)

19. Copyright © 2007 Pearson Education, Inc. Slide R-19 R.5 Adding and Subtracting Like Radicals Solution (b)

20. Copyright © 2007 Pearson Education, Inc. Slide R-20 R.5 Multiplying Radical Expressions Example Find each product. (a) (b) Solution (a) Using FOIL,

21. Copyright © 2007 Pearson Education, Inc. Slide R-21 R.5 Multiplying Radical Expressions Solution (b)

22. Copyright © 2007 Pearson Education, Inc. Slide R-22 R.5 Rationalizing Denominators The process of simplifying a radical expression so that no denominator contains a radical is called rationalizing the denominator. Rationalizing the denominator is accomplished by multiplying by a suitable form of 1.

23. Copyright © 2007 Pearson Education, Inc. Slide R-23 R.5 Rationalizing Denominators Example Rationalize each denominator. (a) (b) Solution (a) (b)

24. Copyright © 2007 Pearson Education, Inc. Slide R-24 R.5 Rationalizing a Binomial Denominator Example Rationalize the denominator of Solution

25. Copyright © 2007 Pearson Education, Inc. Slide R-25 Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pp. 72-76 also the package Homework: Pp. 34 #57-60 Don’t leave your grades to chance…do your homework! R.8 nth Roots and Rational Expressions