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Rationalizing Denominators: Simplify Quotients

Learn how to rationalize denominators by simplifying quotients with square roots in the denominator. Follow step-by-step examples to simplify expressions and simplify square roots in the numerator. Practice rationalizing denominators for better understanding.

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Rationalizing Denominators: Simplify Quotients

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

  2. Objectives Rationalize denominators.

  3. 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.

  4. Directions: Simplify the quotient.

  5. 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.

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

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

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

  9. 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.

  10. Example 6

  11. Lesson Summary Simplify each quotient. 1. 2.

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