1. Rationalizing the Denominator

2. Essential Question How do I get a radical out of the denominator of a fraction?

3. If a fraction has a denominator that is a square root, you can simplify it by rationalizing the denominator. To do this: Multiply both the numerator and the denominator by a number that produces a perfect square under the radical sign in the denominator. TIP: Always look to SIMPLIFY at the beginning of the problem. This usually makes the simplifying or reducing at the end easier!! WE DON’T LEAVE SQUARE ROOTS IN THE DENOMINATOR!!!

4. Example 1 Simplify by rationalizing the denominator:

5. Example 2 Simplify by rationalizing the denominator: Is there a simpler way of doing this problem? Look at the beginning. Can we simplify the original expression?

7. PART II: Using a CONJUGATE to rationalize a binomial denominator A conjugate is… a binomial with the opposite operation. Number pairs in the form a + √(b) and a – √(b) are conjugates. Example: The conjugate of 2 + √(3) is 2 – √(3) Example: The conjugate of –3 – 4 √(5) is –3 + 4√(5) Multiplying a number by its conjugate produces a rational number. Example: (2 + √(3)) (2 – √(3)) = 4 – 2√(3) + 2√(3) – 3 = 1 You try: (-1 + 2√(5)) (-1 – 2√(5)) = 1 + 2√(5) – 2√(5) – 4(5) = 1 – 20 = –19

8. Example 3 Simplify by rationalizing the denominator:

9. Example 4 Simplify by rationalizing the denominator: