1. Worksheet Key
2/23/2019 9:20 PM
Simplifying Radicals

2. Grade Distribution 1st 4th 7th 9th A 9 2 5 B 8 11 4 C 6 D 3 F 7D 3 F 7
No Show 1
100+
Range
48-105
45-99
52-103
41-95
Avg
79.3
76.1
80.56
72.31

3. SIMPLIFYING RADICAL EXPRESSIONS
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Simplifying Radical Expressions

4. Radicals are a way to symbolized a number being rooted
Definitions
Square Roots are a number that when squared (multiplied by itself) is equal to the given number
Radicals are a way to symbolized a number being rooted
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Simplifying Radicals

5. Root Radical Sign Base Review Identifying radicals Unless noted,
we must
assume the
root is 2
Base

6. Review
Identifying radicals
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Simplifying Radicals

7. 10.3 - Simplifying Radical Expressions
STEPS
Identify the root and the base
Breakdown the base to prime and group them into roots OR perfect roots into radical form
Combine all the same radicals
(for example if √5 and √5 comes out, drop off the radical and keep the number [5])
Multiply the bases and radicals together
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Simplifying Radical Expressions

8. 10.3 - Simplifying Radical Expressions
Example 1
Simplify
Identify the root and base
Root
Base
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Simplifying Radical Expressions

9. 10.3 - Simplifying Radical Expressions
Example 1
Simplify
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Simplifying Radical Expressions

10. 10.3 - Simplifying Radical Expressions
Your Turn
Simplify
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Simplifying Radical Expressions

11. 10.3 - Simplifying Radical Expressions
Example 2
Simplify
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Simplifying Radical Expressions

12. 10.3 - Simplifying Radical Expressions
EXAMPLE 3
Simplify
Identify the root and base
Root
Base
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Simplifying Radical Expressions

13. 10.3 - Simplifying Radical Expressions
EXAMPLE 3
Simplify
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Simplifying Radical Expressions

14. 10.3 - Simplifying Radical Expressions
EXAMPLE 4
Simplify
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Simplifying Radical Expressions

15. 10.3 - Simplifying Radical Expressions
Your Turn
Simplify
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Simplifying Radical Expressions

16. 10.3 - Simplifying Radical Expressions
EXAMPLE 5
Simplify
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Simplifying Radical Expressions

17. 10.3 - Simplifying Radical Expressions
Your Turn
Simplify
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Simplifying Radical Expressions

18. 10.3 - Simplifying Radical Expressions
EXAMPLE 6
Simplify
Identify the root and base(s)
Root
Bases
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Simplifying Radical Expressions

19. 10.3 - Simplifying Radical Expressions
EXAMPLE 6
Simplify
Combine like terms if necessary and multiply.
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Simplifying Radical Expressions

20. 10.3 - Simplifying Radical Expressions
Your Turn
Simplify
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Simplifying Radical Expressions

21. 10.3 - Simplifying Radical Expressions
Review
Simplify 3x • 4x
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Simplifying Radical Expressions

22. Steps for Multiplying/Dividing
Multiply only with the same indexes
Reduce radicals to proper simplified form
Simplify
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Simplifying Radical Expressions

23. 10.3 - Simplifying Radical Expressions
Example 7
Simplify 3√2 • 2√2
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Simplifying Radical Expressions

24. 10.3 - Simplifying Radical Expressions
Example 8
Simplify 2√3 • 4√12
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Simplifying Radical Expressions

25. 10.3 - Simplifying Radical Expressions
Your Turn
Simplify
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Simplifying Radical Expressions

26. EXAMPLE 9
Simplify
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Radical Operations

27. 10.3 - Simplifying Radical Expressions
Example 10
Simplify
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Simplifying Radical Expressions

28. EXAMPLE 11 Simplify REMEMBER:
No radicals in the denominator; we must multiply by the radical in denominator
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Radical Operations

29. 10.3 - Simplifying Radical Expressions
Review
Simplify 3x + 4x
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Simplifying Radical Expressions

30. Add/Subtract Radicals
Reduce radicals to proper simplified form
Combine like terms
Simplify, if needed
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Radical Operations

31. 10.3 - Simplifying Radical Expressions
Example 12
Add
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Simplifying Radical Expressions

32. 10.3 - Simplifying Radical Expressions
Example 13
Add
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Simplifying Radical Expressions

33. 10.3 - Simplifying Radical Expressions
Example 14
Subtract
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Simplifying Radical Expressions

34. 10.3 - Simplifying Radical Expressions
Your Turn
Subtract
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Simplifying Radical Expressions

35. 10.3 - Simplifying Radical Expressions
Example 15
Simplify
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Simplifying Radical Expressions

36. 10.3 - Simplifying Radical Expressions
Example 16
Simplify
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Simplifying Radical Expressions

37. 10.3 - Simplifying Radical Expressions
Your Turn
Simplify
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Simplifying Radical Expressions

38. EXAMPLE 17
Simplify
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Radical Operations

39. EXAMPLE 18
Simplify
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Radical Operations

40. YOUR TURN
Simplify
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Radical Operations

41. Review
Multiply FOIL

42. Example 19
Multiply
What’s another way of re-writing this?

43. Example 20
Multiply
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Multiplying Radicals

44. Your Turn
Multiply

45. Example 21
Multiply

46. Your Turn
Multiply