1. 5-6 Radical Expressions Objectives Students will be able to: 1)Simplify radical expressions 2)Add, subtract, multiply, and divide radical expressions

2. Up to this point, we have only dealt with perfect squares, cubes, etc. as our radicands. How would we simplify a radical expression that does not have a perfect value as a radicand? Let’s examine first how to simplify square roots. The same steps could be applied to simplifying cubed roots, fourth roots, etc…

3. Steps to simplify a square root. 1)Factor the radicand into as many squares as possible. 2)Isolate the perfect square terms. 3)Simplify each radical.

4. Example 1: Simplify each expression. 1)2) 3)4)

5. Try these. 5)6)

6. Now let’s tie in variables. Example 2: Simplify each expression. 1)2) 3)

7. Try these. 4)5)

8. Adding and subtracting radicals is very similar to adding and subtracting monomials. Remember, to add or subtract monomials, you need the same variables and same exponents on those variables (like terms). To add or subtract radical expressions, you need the same radicand and same index (like radical expressions) If the terms have the same radicand and same index, you add/subtract the terms on the outside of the radical expression, and keep the index and radicand. You may need to simplify the terms before you can add/subtract.

9. Example 3: Simplify. 1)2) 3)4)

10. Try these. 5)6)

11. When multiplying radical expressions, the terms on the outside of the radicals get multiplied, and the radicands get multiplied. You then simplify, if possible. – If you choose, you can simplify the radical expressions first (if possible), and then multiply. EXAMPLE TIME!!!

12. Example 4: Simplify. 1)2) 3)4)

13. Try these. 5)6)

14. 7) 8)

15. 9)

16. Try these. 10) 11)

17. There can never be a radical in the denominator of a fraction. If a denominator contains a radical, the expression must be rationalized. This occurs by multiplying the entire expression by a form of the number 1. The goal is to multiply by a quantity so that the radicand has an exact root. Let’s see what this all means…

18. Example 5: Simplify. 1) 2) 3)4)

19. 5)6) Try these. 7)8)

20. 9) 10)

21. Try this. 11)