Chapter 5

1. Chapter 5 Section 5.6

2. Objectives • To simplify radical expressions. • To rationalize the denominator of a fraction containing a radical expression. • To add, subtract, multiply, and divide radical expressions.

3. Product Property of Radicals For any real numbers a and b, and any integer n, n > 1: • If n is even, then (ab) =(a) * (b) when a and b are both nonnegative, and • If n is odd, then (ab) =(a) * (b). n n n n n n

4. Example Simplify 81p4q3 Answer: 9p2q(q)

5. Example Simplify 727n2 * 48n Answer: 168n 3 3

6. Quotient Property of Radicals For real numbers a and b, b  0, any integer n, n>1, = , if all roots are defined.

7. Conditions • The index, n, is as small as possible. • The radicand contains no factors (other than 1) that are nth powers of an integer or polynomial. • The radicand contains no fractions. • No radicals appear in the denominator.

8. Rationalizing the Denominator • To eliminate radicals from a denominator or fractions from a radicand, you can use the process called rationalizing the denominator.

9. Example Simplify Answer:

10. Radical Expressions Two radical expressions are called like radical expressions if both the indices and the radicands are alike. Examples: 6 - 17 3 +

11. Example Simply 2 - 2 + 3 Answer: 10

12. Practice Pg 293 9 – 21 [odd]