Chapter 8: Inverses and Radicals Lesson 6: Quotients with Radicals Mrs. Parziale

Quotients with Radicals Given the fraction: To write an equivalent form with a rational number as the denominator: Multiply both the numerator and the denominator by Does this change the value of the fraction? Find decimal approximations of and the final rationalized equivalent. Conclusion: Rationalizing the denominator of a fraction means: write an ____________________ form of the fraction with a rational number as the denominator. equivalent Example 1: NO They are the same value.

Rationalizing the Denominator Example 2: Rewrite each expression without a radical sign in the denominator: To rationalize the denominator of a fraction whose denominator is multiply both the numerator and denominator by (a > 0) because.

Example 2, cont. Conclusion: For all positive numbers x: Conclusion: For all positive numbers x: Rewrite each expression without a radical sign in the denominator:

Example 3 Rationalize the denominator in the fraction: where x > 0 Simplify first and then rationalize the denominator.

Example 3, cont. Rationalize the denominator in the fraction: where x > 0 Rationalize the denominator first and then simplify.

To simplify a denominator of the form multiply it by its conjugate or Example 4: Rewrite the expression without a radical sign in the denominator: a)

Example 4, cont. b) c)

Closure Why do we rationalize the denominator? Explain how to rationalize the denominator in this example: Simplify and rationalize the following expression: