1. Multiplying & Simplifying Radical Expressions
KM & PP 1 1

2. Finding
Square Roots
Definition
8.2 S
KM & PP

3. Remember!
The Square Root
of Apple Squared
is Apple!
8.2 S
KM & PP

4. Notice!
AND
8.2 S
KM & PP 4

5. Notice!
8.2 S
KM & PP 5

6. The Product Rule for Radicals.
The product of square roots is the square root of the product of the radicands AB of nonnegative radicands A & B.
8.2 S
KM & PP

7. The Product Rule for Radicals.
EXAMPLES: Multiply
8.2 S
KM & PP 7

8. Radical Expressions.
How about?
8.2 S
KM & PP

9. Radical Expressions.
Check the definition
8.2 S
KM & PP

10. Check: x3x3=x3+3=x6 Check: x6x6=x6+6=x12 Try Two! Examples 4 & 5 8.2 S
KM & PP

11. Notice a Pattern?
8.2 S
KM & PP

12. Notice a Pattern?
8.2 S
KM & PP

13. You try. Example 6
Check: x17x17=x17+17=x34
8.2 S
KM & PP

14. You try. Example 7
Check: x31x31=x31+31=x62
8.2 S
KM & PP 14

15. Notice!
8.2 S
KM & PP

16. Factoring Radical Expressions.
KM & PP

17. Factoring Radical Expressions.
EXAMPLES: Simplify
8.2 S
KM & PP 17

18. How About?
8.2 S
KM & PP

19. Introduction to Radical Expressions.
Even exponents are squares.
Odd exponents can be factored to even exponents times x.
8.2 S
KM & PP

20. In Other Words The Square Root of Apple Cubed is Apple times
KM & PP

21. You Try. Example 9
8.2 S
KM & PP

22. You Try. Example 10
8.2 S
KM & PP

23. More Problems. Example 11
8.2 S
KM & PP

24. More Problems. Example 12
8.2 S
KM & PP

25. One More. Example 13
8.1 S
KM & PP

26. Another Square Root! Example 16
KM & PP

27. More Problems. Example 17
8.2 S
KM & PP

28. Factoring Again. Example 17
8.2 S
KM & PP

29. The Product Rule for Radicals Basics
Simplify After Multiplying.
Leave the Radicand in Factored Form.
Factor Further to find Perfect-square factors.
Simplify using the perfect-square factors.
8.2 S
KM & PP

30. The Product Rule for Radicals.
EXAMPLE 18: Multiply
8.2 S
KM & PP 30

31. The Product Rule for Radicals.
Another Approach
EXAMPLE 18: Multiply
8.2 S
KM & PP 31

32. Remember! One gets shot during the escape. The Radical is
like a prison.
It takes two
to escape.
8.2 S
KM & PP 32 32

33. The Product Rule for Radicals.
EXAMPLE 19: Multiply
8.2 S
KM & PP 33

34. The Product Rule for Radicals.
Another Approach
EXAMPLE 19: Multiply
8.2 S
KM & PP 34

35. That’s All for Now!
8.1 S
KM & PP