1. Warm-Up: HW #5: Simplifying radicals Agenda WU (10 min)
SWBAT…simplify radicals using the product property of radicals Wed, 3/14
Agenda
WU (10 min)
Lesson on product property of radicals – 13 examples! (30 min)
Warm-Up:
HW #5: Simplifying radicals

2. Simplifying Radical Expressions

3. Properties of Radicals

4. In the expression , is the radical sign and 64 is the radicand.

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

6. Product Property of Radicals
(13 examples)

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

8. 1. Simplify

9. Find a perfect square that goes into 147.
2. Simplify
Find a perfect square that goes into 147.

10. 3. Simplify

11. Find a perfect square that goes into 605.
4. Simplify
Find a perfect square that goes into 605.

12. 5. Simplify .

13. 6. Simplify
6b. Simplify
As a general rule, divide the exponent by two. The remainder stays in the radical.

14. 7. Simplify

15. 8. Simplify
As a general rule, divide the exponent by two. The remainder stays in the radical.

16. 9. Simplify
As a general rule, divide the exponent by two. The remainder stays in the radical.

17. 10. Simplify
3x6
3x18
9x6
9x18
As a general rule, divide the exponent by two. The remainder stays in the radical.

18. 11. Simplify
Multiply the radicals.

19. Multiply the coefficients and radicals.
12. Simplify
Multiply the coefficients and radicals.

20. 13. Simplify .

21. SWBAT…simplify radicals using the quotient of property of radicals
Agenda
WU (10 min)
Lesson on quotient property of radicals – 5 examples (20 min)
Lesson on adding and subtracting radicals – 6 examples (15 min)
Warm-Up: 1.
HW #7: Quotient Property of Radicals

22. Quotient Property of Radicals
(5 examples)

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

24. Examples:

25. Rationalizing the denominator
Rationalizing the denominator means to remove any radicals from the denominator.
3. Simplify

26. 4. Simplify

27. Simplify 5.

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

29. = 6
= 3
= 2

30. Adding and Subtracting Radicals (6 examples)

31. Sums and Differences
Rules in the previous section allowed us to split radicals that had a radicand which was a product or a quotient.
However, we can NOT split sums or differences.

32. Adding and Subtracting Radicals
We can only combine terms with radicals
if we have like radicals
Ex 1
Ex 2
Ex 3
Simplified

33. Adding and Subtracting Radicals
Ex 4

34. Adding and Subtracting Radicals
Ex 5
Simplify the following radical expression.

35. Ex 6