1. Laws of Exponents (Warm-Up)
(1)
(2)
(3)

2. Homework
Go over homework answers/problems

3. Radicals

4. Radicals
Radicand
Index
COEFFICIENT

5. Simplifying Radicals
"Roots" (or "radicals") are the "opposite" operation of applying exponents; you can "undo" a power with a radical, and a radical can "undo" a power. 
For instance, if you square 2, you get 4, and if you "take the square root of 4", you get 2; if you square 3, you get 9, and if you "take the square root of 9", you get 3.
So does anybody know what we call numbers like: 4, 9, 16, 25, 36, 49…..  

6. So what are the “Perfect Squares”?

7. Steps to Simplifying Radicals (that are not perfect squares)
Simplifying Radicals that are square roots
Create a factor tree
Identify any factor that is a perfect square
That perfect square “pair” will come outside the radical and be multiplied by the existing coefficient
All other factors will remain inside the radical as part of the radicand

8. Simplifying Radicals

9. 200 𝑣 7 𝑟 10
28𝑥 4

10. What about if the Index Changes?

11. Adding and Subtracting Radicals
Must have the same radicand and index
Only add and subtract the number outside the radical

12. Adding and Subtracting Radicals

13. Adding and Subtracting Independent Practice

14. More Practice Adding and Subtracting

15. Multiplication of Radicals
Multiplying Radicals
only need same index to multiply
multiply numbers on the outside of the radical separately than numbers on the inside of the radical
must simplify the final answer as far as possible

16. Multiplication of Radicals

17. Multiplication of Radicals

18. Multiplication of Radicals
Multiplying Radicals
only need same index to multiply
multiply numbers on the outside of the radical separately than numbers on the inside of the radical
must simplify the final answer as far as possible

19. Warm-Up Problems & Homework
𝑥 7 𝑥 (2) (−3 𝑧 2 ) 2 (3) 28𝑥 −2 7𝑦 −3
(4) (−2 𝑟 −4 𝑠 2 ) −3 (5) Simplify 525
(6) Simplify 𝑥 5 𝑦 6

20. Multiplication of Radicals

21. What Happens When…. We Square a Radical Term?
We Square a Binomial with a Radical?
We are asked to Multiply a Binomial with a Radical by another Binomial with a Radical?

22. Multiplication of Radicals
( 4 𝑥 2 𝑦 −2𝑥 ) 2

23. More Practice Multiplying Radicals

24. Division of Radicals Dividing radicals
Cannot have a fraction under a radical
Cannot have a radical in the denominator
(called rationalizing the denominator)
Multiply top and bottom by the bottom radical
Simplify your answer

25. Division of Radicals

26. Division of Radicals Practice

27. More Practice With Division of Radicals

28. Worksheet Division of Radicals

29. REVIEW PROBLEMS 1)

30. REVIEW PROBLEMS 6)
−6 5− 6

31. SOLVING RADICAL EQUATIONS

32. Solving Simple Radical Equations
So, if we try to solve… 𝑦 = 5 …… then what is y?
And if 2𝑥 = 8 …. then what is x = ?

36. Challenge Problems Solve for x 3𝑥 = 9 Solve for y 4 𝑦 −1 = -8 (2) (1)
(4)
(3)
Solve for x
3𝑥 = 9
Solve for y
4 𝑦 −1 = -8

38. YOUR TURN
Solve: 𝑥 = 2
Solve: 9𝑦 = 12
𝑚 4 = 3

39. Solving Radical Equations
𝑥 − = 5 (4) 𝑣+15 = 𝑣
so what happens if the equation
has more than one radical?
3𝑧 −5 = 4 (5) 𝑥+12 − 𝑥 = 3
𝑥 −15 = 𝑥 (6) 9𝑛− 𝑛−1 = 3

40. Worksheet on ALEKS
REVIEW and Solving Radical Equations

41. Applications of Radical Equations
(1)
(2)

42. Rational Exponents

43. Rational Exponents
𝑛 𝑎 𝑚 = 𝑎 𝑚 𝑛
and

44. RATIONAL EXPONENTS

45. RATIONAL EXPONENTS

46. RATIONAL EXPONENTS

47. RATIONAL EXPONENTS