2. Objectives The student will be able to: 1. simplify square roots, and 2. simplify radical expressions.

3. In the expression, is the radical sign and 64 is the radicand. If x 2 = y then x is a square root of y. 1. Find the square root: 8 2. Find the square root: -0.2

4. 11, -11 4. Find the square root: 21 5.Find the square root: 3. Find the square root:

5. 6.82, -6.82 6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth.

6. 1 1 = 1 2 2 = 4 3 3 = 9 4 4 = 16 5 5 = 25 6 6 = 36 49, 64, 81, 100, 121, 144,... What numbers are perfect squares?

7. 1. Simplify Find a perfect square that goes into 147.

8. 2. Simplify Find a perfect square that goes into 605.

9. Simplify 1.. 2.. 3.. 4..

10. Look at these examples and try to find the pattern… How do you simplify variables in the radical? What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

11. Find a perfect square that goes into 49. 4. Simplify 5. Simplify

12. Simplify 1.3x 6 2.3x 18 3.9x 6 4.9x 18

13. Multiply the radicals. 6. Simplify

14. 7. Simplify Multiply the coefficients and radicals.

15. Simplify 1.. 2.. 3.. 4..

16. How do you know when a radical problem is done? 1.No radicals can be simplified. Example: 2.There are no fractions in the radical. Example: 3.There are no radicals in the denominator. Example:

17. 8. Simplify. Divide the radicals. Uh oh… There is a radical in the denominator! Whew! It simplified!

18. 9. Simplify Uh oh… Another radical in the denominator! Whew! It simplified again! I hope they all are like this!

19. 10. Simplify Since the fraction doesn’t reduce, split the radical up. Uh oh… There is a fraction in the radical! How do I get rid of the radical in the denominator? Multiply by the “fancy one” to make the denominator a perfect square!

20. Product Property of Radicals For any numbers a and b where and,

21. Product Property of Radicals Examples

22. Examples:

24. Quotient Property of Radicals For any numbers a and b where and,

25. Examples:

27. Simplest Radical Form No perfect nth power factors other than 1. No fractions in the radicand. No radicals in the denominator.

28. Adding radicals We can only combine terms with radicals if we have like radicals Reverse of the Distributive Property

29. Examples:

31. Multiplying radicals - Distributive Property

32. Multiplying radicals - FOIL F O I L

33. Examples: F O I L

34. F O I L

35. Conjugates Binomials of the form where a, b, c, d are rational numbers.

36. The product of conjugates is a rational number. Therefore, we can rationalize denominator of a fraction by multiplying by its conjugate.

37. Examples: