1. HOME ROOM

2. BELL-WORK Use your calculator to simplify (a) √2 •√2 (b) √5 •√5
Do you notice a pattern?

3. Square Property of Square Roots

4. CW 4.6 Review
TB pg 616 # 17, 19, 25, 29

5. Materials Check

6. Due tomorow: PW 10-3 # 13-18(odd), 19-24
HW 4.4(c)
Due tomorow:
PW 10-3 # 13-18(odd), 19-24

7. HW 4.4(b) Solutions

8. Guiding question:
What is a simplified radical?

9. RECALL A simplified radical: Has no perfect square as its factor
Has no radicals in the denominator
We have discussed the multiplication property of square roots, now we will now discuss some other properties of square roots that will help us to simplify an expression that has a radical in the denominator.

10. Square Property of Square Roots9

11. Square Property of Square Roots3

12. Square Property of Square Roots12

13. Division Property of Square Roots
a ≥ 0, b > 0

14. Division Property of Square Roots
Example:

15. Division Property of Square Roots
Example:

16. Division Property of Square Roots
Example:

17. Division Property of Square Roots
Example:
Is this a simplified radical?

18. Division Property of Square Roots
Example:
Is this a simplified radical?
What can be done to get rid of the radical in the denominator?

19. Division Property of Square Roots
Example:

20. Division Property of Square Roots
Example:

21. Division Property of Square Roots
Example:
*This process is known as
rationalizing the
denominator.

22. Division Property of Square Roots
Simplify:

23. Division Property of Square Roots
Simplify:

24. Division Property of Square Roots
Simplify:

25. Division Property of Square Roots
Simplify:

26. Division Property of Square Roots
Simplify:

27. Division Property of Square Roots
Simplify:

28. Simplifying Radicals Multiply (√5 – √2)(√5 + √2)
Does this type of multiplication problem look familiar?
DOTS
(a – b)(a + b) =
a2 – b2
(√5 – √2)(√5 + √2)
(√5)2 – (√2)2
5 – 2 3

29. Conjugate Property of Square Roots
a ≥ 0, b ≥ 0

30. Conjugate Property of Square Roots
Multiply (√6 – 3√21)(√6 + 3√21)
(√6)2 – (3√21)2
6 – 9•21
-183
(√7 – 4√13)(√7 + 4√13)
(√7)2 – (4√13)2
7 – 16•13
-201

31. Simplifying Radicals
Simplify:

32. Simplifying Radicals Simplify:
What can be done to get rid of the radicals in the denominator?

33. Simplifying Radicals
Simplify:

34. Simplifying Radicals
Simplify:
= 8√7 + 8√3
7 – 3

35. Simplifying Radicals
Simplify:
= 8√7 + 8√3
7 – 3 4

36. Simplifying Radicals
Simplify:
= 8√7 + 8√3
7 – 3 4
= 2√7 + 2√3

37. Rationalizing the Denominator
To simplify an expression with a radical in the denominator multiply by the radical.
To simplify an expression with a sum or difference of radicals in the denominator, multiply by the conjugate of the denominator.

38. Simplifying Radicals
Simplify:

39. Simplifying Radicals
Simplify:

40. Simplifying Radicals
Simplify:
= 9√12 – 9√11
12 – 11

41. Simplifying Radicals
Simplify:
= 9√12 – 9√11
12 – 11

42. Simplifying Radicals
Simplify:
= 9√12 – 9√11
12 – 11
= 18√3 – 9√11

43. Simplifying Radicals
Complete TB pg 616 # 30,31,33

44. Who wants to answer the Guiding question?
What is a simplified radical?

45. CW 4.7
Detach a sheet of notebook paper from the CW section of your notebook.
Complete:
TB pg 616 # 9,15,21,28,29