1. 5-5 ROOTS OF REAL NUMBERS Objective: Students will be able to simplify radicals.

2. Terminology  Index: tells us what root we are looking for  Radicand: term underneath the radical sign

3. To Find the ROOT of a VARIABLE…  divide the exponent on the variable by the index.  Examples:

4. Find the roots of each of the following: 1) 2)3) 4)5)6)

5. COMMON ROOTS

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

7. 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.

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

9. Try these. 4)5)

10.  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.

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

12. Try these: 5)6)

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

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

15. Try these. 5)6)

16. 7) 8)

17. 9)

18. Try these. 10) 11)

19.  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…

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

21. 5)6) Try these. 7)8)

22. 9) 10)

23. Try this. 11)