1. Objective: Add, subtract and multiplying radical expressions; re-write rational exponents in radical form. Essential Question: What rules apply for adding, subtracting and multiplying radicals? What are rational exponents?

2. Parts of a radical expression:

3. Part 1: How to Simplify  1. Make a factor tree  2. Circle groups of  Two (square root)  Three (cube root)  Four (fourth root)  Move one number from each group to the outside

4. Simplify

7. Part 2: Rational Exponents  Rational Exponents:  Exponents that are written as fractions

8. Re-write in radical form

15. Part 3: Multiplying  You cannot multiply radicals if the indexes are different  Multiply the coefficients and radicands  Simplify answer by making a factor tree

16. Multiply & Simplify

18. Part 4: Adding & Subtracting  You cannot add/subtract radicals if the indexes or radicands are different  Simplify by making a factor tree first  Add coefficients, keep the radicand the same

19. Combined expressions:

21. You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

22. You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

23. You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

24. You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

25. You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

26. You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined: