CHAPTER_ppt_10_5 - -). Conjugates Martin-Gay, Beginning and...

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§ 10.5 Rationalizing Numerators and Denominators of Radical Expressions
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Many times it is helpful to rewrite a radical quotient with the radical confined to ONLY the numerator. If we rewrite the expression so that there is no radical in the denominator, it is called rationalizing the denominator . This process involves multiplying the quotient by a form of 1 that will eliminate the radical in the denominator. Rationalizing the Denominator
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Rationalize the denominator. 2 3 = 2 2 3 9 6 = 3 3 3 3 = 2 2 2 3 2 6 = 3 3 3 3 9 3 6 = 3 3 27 3 6 = 3 3 6 3 3 3 2 Rationalizing the Denominator Example:
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Many rational quotients have a sum or difference of terms in a denominator, rather than a single radical. In that case, we need to multiply by the conjugate of the numerator or denominator (which ever one we are rationalizing). The conjugate uses the same terms, but the opposite operation (+ or
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Unformatted text preview: -). Conjugates Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Rationalize the denominator. 3 2 2 3 + + 2 3 3 2 3 2 2 2 3 2 3 2 2 3 2 3 3-- +- =-- + -6 3 2 2 2 3 2 3- +-=-6 3 2 2 2 3 1- +-=-6 3 2 2 2 3 = -+ -+ Rationalizing the Denominator Example: Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 An expression rewritten with no radical in the numerator is called rationalizing the numerator . 12 7 12 7 = 12 12 12 2 21 = 12 12 7 12 = 12 84 = 12 4 21 = 12 4 21 = 6 21 = Rationalizing the Numerator Example: Martin-Gay, Beginning and Intermediate Algebra, 4ed 7 Rationalize the numerator. 3 9 7 y 3 3 9 7 y = 2 3 2 3 3 3 y y 2 3 3 2 3 3 9 3 7 3 y y y = 3 3 2 3 27 21 y y = 2 3 3 21 y y = y x y x-+ x y x y--x xy xy y x xy xy y-+-=--+ x x y x y y x x y x y y- + -=-- + 2 x y x xy y-=-+ Rationalizing the Numerator Example:...
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CHAPTER_ppt_10_5 - -). Conjugates Martin-Gay, Beginning and...

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