1. 7.7 Operations with Radicals

2.  A or of radicals can be simplified using the following rules.  1. Simplify each in the sum.  2. Then, combine radical terms containing the same and. sumdifference radical index radicand

3. Simplify. 1.2.

4. Simplify. 3.4.

5. Simplify. 5.6.

6.  To rationalize a denominator containing two terms, we need to multiply the numerator and denominator by the of the denominator.  Conjugates of radical expressions involve the sum or difference of the same two terms.  Example: and conjugate

7. How Does This Work??  Multiply the conjugates below:

8. Multiplying Conjugates *Think difference of squares!

9. Simplify. 7. 8.

10.  We use this idea to rationalize a denominator because it gets rid of the. radical

11. Simplify. 9.

12. Simplify. 10.

13. Simplify. 11.

14. Simplify. 12.