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Warm Up Simplify each expression. 1. 2. 3. 4.

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Objectives Rationalize denominators.

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**A quotient with a square root in the denominator is not simplified**

A quotient with a square root in the denominator is not simplified. To simplify these expressions, multiply by a form of 1 to get a perfect-square radicand in the denominator. This is called rationalizing the denominator.

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**Directions: Simplify the quotient.**

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Example 1 Multiply by a form of 1 to get a perfect-square radicand in the denominator. Product Property of Square Roots. Simplify the denominator.

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Example 2 Multiply by a form of 1 to get a perfect-square radicand in the denominator. Simplify the square root in denominator.

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Example 3 Multiply by a form of 1 to get a perfect-square radicand in the denominator. Simplify the square root in denominator.

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Example 4 Multiply by a form of 1 to get a perfect-square radicand in the denominator. Simplify the square root in denominator.

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Example 5 Multiply by a form of 1 to get a perfect-square radicand in the denominator. Simplify the square root in denominator. Factor and simplify the square root in the numerator.

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Example 6

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Lesson Summary Simplify each quotient. 1. 2.

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