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Chapter 5

Chapter 5. Section 5.6. Objectives. To simplify radical expressions. To rationalize the denominator of a fraction containing a radical expression. To add, subtract, multiply, and divide radical expressions. Product Property of Radicals.

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Chapter 5

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  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]

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