Rationalizing Numerators and Denominators of Radical Expressions 8.5
Rationalizing Denominators You may not have a radical in the denominator. Example: 8 5 Nor may you have a fraction in a radical. Example: 2 3
Simplifying Fractions with a Radical in the Denominator ( Numerator ) In short, multiply the denominator by the smallest value to make the denominator a perfect n th root. “ To rationalize a denominator containing a single n th root, multiply the fraction by a well chosen “1” so that the product’s denominator has a radicand that is a perfect n th power.”
Examples 8 a. 5 2 b. 3 3 6 c. x y 3 3 9 x y d . 7 3 2 16 x
Sums/Differences in Denominator Some radicals have either a sum or difference in the denominator. Examples: 7 3 5 12 5 11 3
Simplifying with Sums/Differences in the Denominator Multiply the numerator and denominator by the conjugate of the denominator. “To rationalize a denominator containing a sum or difference with at least one square root term, multiply the fraction by a 1 whose numerator and denominator are the conjugate of the denominator.”
Examples 7 a. 3 5 12 5 b. 11 3 4 c . 3 x
Rationalizing Numerators and Denominators of Radical Expressions 8.5
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