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Adding, Subtracting, and Multiplying Radical Expressions

In this chapter, you will learn how to add, subtract, and multiply radical expressions. You will also learn how to simplify expressions before performing operations and how to rationalize binomial radical denominators.

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Adding, Subtracting, and Multiplying Radical Expressions

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  1. Chapter 6 Radical Functions and Rational Exponents

  2. 6-3 Binomial Radical Expressions What you’ll learn … • To add and subtract radical expressions • To multiply and divide binomial radical expressions • 1.01 Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems.

  3. Like radicals are radical expressions that have the same index and the same radicand. To add or subtract like radicals, use the Distributive Property.

  4. Example 1 Adding and Subtracting Radical Expressions 5 √ x - 3 √ x 4 √ xy + 5 √ xy 4 √ 2 - 5 √ 3 7 √ 5 - 2 √5 2 √ 7 + 3 √ 7 3 3 3 4

  5. Example 2 Simplifying Before Adding or Subtracting 6 √ 18 + 4 √ 8 - 3√ 72 √ 50 + 3 √ 32 - 5 √ 18

  6. Example 4 Multiplying Binomial Radical Expressions (3 + 2√ 5 ) ( 2 + 4 √ 5 ) (√ 2 - √ 5 ) 2

  7. Example 5 Multiplying Conjugates (2 + √ 3 ) ( 2 - √ 3 ) (√ 2 - √ 5 ) (√ 2 + √ 5 )

  8. 3 + √5 1 - √5 6 + √15 4 - √15 Example 6 Rationalizing a Binomial Radical Denominator

  9. Homework • p378 • # 13-19, • 25-36, • 38, 43, 46 • Quiz on Friday • Assignment due on Monday

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