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
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.