1. Warm-up Simplify 1.6 2 2.(-14) 2 3.-9 2 4.0 2 1.36 2.196 3.-81 4.0

2. Simplifying Radicals

3. Essential Question How do I evaluate and approximate square roots?

4. Square root of a # If b 2 = a, then b is a square root of a. Example: if 3 2 = 9, then 3 is a square root of 9

5. Definition of Square Root If a is a # greater than or equal to zero, the represents the principal, or positive, square root of a and a negative sq. rt. is represented by Examples:

6. Radical and Radicand What are they? Radical sign Radicand: # or expression under radical symbol Positive or Negative

7. Perfect Squares Numbers whose square roots are integers or quotients of integers. Examples: 4, 16, 25, 100, ¼

8. Example 1 Simplify = 4 = -5

9. What if the radicand is not a perfect square? You can do one of 2 things… –Give an approximation –Give a simplified exact answer Read the directions to see which one you should do!

10. 2 Example 1 Simplify. Give an exact answer. Now circle your pairs! 22 Pull out one number and throw out the other one. Write the prime factorization of 8! What is left?

11. 2 Example 2 Simplify. Give an exact answer. Now circle your pairs! 23 Pull out one number and throw out the other one. Write the prime factorization of 24! What is left? 2

12. Example 3 2225 Write the prime factorization of 80! Simplify. Give an exact answer. 2 Now circle your pairs! Pull out one number from each pair and throw out the other ones. What is left?

13. Example 4 Simplify. Give an exact answer.

14. Product Property The square root of a product equals the product of the square roots of the factors. Example:

15. Example 1 (Simplify) Now simplify!!

16. Example 2 (Simplify) a. b.

17. Distribute. Multiply/distribute. This is simplified. Can’t add. Radicands are different.

18. Use FOIL Multiply. F irst O utside I nside L ast Always write number term before radical term!

19. Quotient Property The square root of a quotient equals the quotient of the square roots of the numerator and the denominator. Example:

20. Example 1 (Simplify)

21. Rationalizing Denominators For example.. It is perfectly fine to have a radical in your NUMERATOR. It is NOT o.k. to leave a radical in your DENOMINATOR!

22. Example 2 (Simplify) This is just a fancy form of the number 1

23. Example 3 (Simplify)

24. Example 6 You don’t have to rationalize. Just divide!!

25. Conjugates ExpressionConjugate Product

26. Example

27. ≈ 8.83 Example 5 Give and approximation. Round to the nearest hundredth.

28. Example 6 Give and approximation. Round to the nearest hundredth. ≈ 4.24

29. Homework Page 144 –Numbers 1-12 all, 14, 16, 22.