mgb5e_ppt_8_4

# mgb5e_ppt_8_4 - 2 3 = ⋅ 2 2 3 9 6 = ⋅ 3 3 3 3 = ⋅ ⋅...

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§ 8.4 Multiplying and Dividing Radicals

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Martin-Gay, Beginning Algebra, 5ed 2 n n n ab b a = n a n b If and are real numbers, Product Rule for Radicals
Martin-Gay, Beginning Algebra, 5ed 3 Simplify the following radical expressions. = x y 5 3 xy 15 = 2 3 6 7 b a b a = 2 3 6 7 b a b a = 4 4 b a 2 2 b a Multiplying Radical Expressions Example:

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Martin-Gay, Beginning Algebra, 5ed 4 0 if = b b a b a n n n n a n b If and are real numbers, Quotient Rule for Radicals
Martin-Gay, Beginning Algebra, 5ed 5 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 Algebra, 5ed 6 Rationalize the denominator.

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Unformatted text preview: 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: Martin-Gay, Beginning Algebra, 5ed 7 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 -). Conjugates Martin-Gay, Beginning Algebra, 5ed 8 Rationalize the denominator. 3 2 2 3 + + =-⋅ + ⋅--+-⋅ =--⋅ 3 3 2 3 2 2 3 2 2 2 3 2 3 3 2 3 2 =--+-3 2 3 2 2 2 3 6 =--+-1 3 2 2 2 3 6 3 2 2 2 3 6 +-+-Rationalizing the Denominator Example:...
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mgb5e_ppt_8_4 - 2 3 = ⋅ 2 2 3 9 6 = ⋅ 3 3 3 3 = ⋅ ⋅...

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