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Chapter 8

Chapter 8. Section 4. Rationalizing the Denominator. Rationalize denominators with square roots. Write radicals in simplified form. Rationalize denominators with cube roots. 8.4. 2. 3. Objective 1. Rationalize denominators with square roots. Slide 8.4-3.

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Chapter 8

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  1. Chapter 8 Section 4

  2. Rationalizing the Denominator Rationalize denominators with square roots. Write radicals in simplified form. Rationalize denominators with cube roots. 8.4 2 3

  3. Objective 1 Rationalize denominators with square roots. Slide 8.4-3

  4. It is easier to work with a radical expression if the denominators do not contain any radicals. Rationalize denominators with square roots. This process of changing the denominator from a radical, or irrational number, to a rational number is called rationalizing the denominator. The value of the radical expression is not changed; only the form is changed, because the expression has been multiplied by 1 in the form of Slide 8.4-4

  5. Rationalize each denominator. EXAMPLE 1 Rationalizing Denominators Solution: Slide 8.4-5

  6. Objective 2 Write radicals in simplified form. Slide 8.4-6

  7. Write radicals in simplified form. Conditions for Simplified Form of a Radical 1. The radicand contains no factor (except 1) that is a perfect square (in dealing with square roots), a perfect cube (in dealing with cube roots), and so on. 2. The radicand has no fractions. 3. No denominator contains a radical. Slide 8.4-7

  8. EXAMPLE 2 Simplifying a Radical Simplify Solution: Slide 8.4-8

  9. Simplify EXAMPLE 3 Simplifying a Product of Radicals Solution: Slide 8.4-9

  10. Simplify. Assume that p and q are positive numbers. EXAMPLE 4 Simplifying Quotients Involving Radicals Solution: Slide 8.4-10

  11. Objective 3 Rationalize denominators with cube roots. Slide 8.4-11

  12. Rationalize each denominator. EXAMPLE 5 Rationalizing Denominators with Cube Roots Solution: Slide 8.4-12

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