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May 20, 2023 108 likes •198 views

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

SLIDE 1

Rationalizing Numerators and Denominators of Radical Expressions

8.5

SLIDE 2

Rationalizing Denominators

You may not have a radical in the denominator. Example: Nor may you have a fraction in a radical. Example:

5 8

3 2

SLIDE 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 nth root. “To rationalize a denominator containing a single nth

root, multiply the fraction by a well chosen “1” so that the product’s denominator has a radicand that is a perfect nth power.”

SLIDE 4

Examples

a. b. c. d. 5 8

3 2

3 3 3

9 6 y x y x

3 2

7 16x

SLIDE 5

Sums/Differences in Denominator

Some radicals have either a sum or difference in the denominator. Examples:

7 3 5

12 5 11 3

SLIDE 6

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.”

SLIDE 7

Examples

a. b. c.

7 3 5

12 5 11 3 4 3 x

SLIDE 8