1. Sponge
What operation does each term represent? Create an example for each.
1. Sum
2. Difference
3. Twice
4. Decreased
5. Together
6. Square

2. Radical Sign (square root sign)
Radicand
Numbers or variables under the radical sign

3. Prime Numbers
What type of numbers are these? …

4. Perfect Squares Copy! 64
225 1 81
256 4
100
289 9
121 16
324
144 25
400
169 36
196 49
625

5. Simplify
= 2
= 4
= 5
This is a piece of cake!
= 10
= 12

6. Radicals are in SIMPLEST FORM when..
1. No perfect square factors other than 1 are under the radical.
No fractions are under the radical.
No radicals are in the denominator.

7. Let’s review! Factor Trees to Prime Factorization45

8. Let’s review! Factor Trees to Prime Factorization54

9. When you have a pair, bring the number out.
EX:1 Simplify.
When you have a pair, bring the number out.

10. EX:3

11. When you have a pair, bring the number out.
EX:2 Simplify
When you have a pair, bring the number out.

12. EX:4 Simplify.

13. You try!

14. Sponge

15. = Simplify = = = = = = = = = Perfect Square Factor * Other Factor
Get Ready! =
Simplify = = =
LEAVE IN RADICAL FORM = = = = = =

16. Examples with variables:

17. Examples:

18. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

19. + To combine radicals: combine the coefficients of like radicals
Combining Radicals +
To combine radicals: combine the coefficients of like radicals

20. Simplify each expression

21. Simplify each expression: Simplify each radical first and then combine.

22. Simplify each expression: Simplify each radical first and then combine.

23. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

24. Simplify each expression

25. Simplify each expression

26. Multiplying Radicals *
To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

27. Multiply and then simplify

29. Dividing Radicals
To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

30. That was easy!

31. 42 cannot be simplified, so we are finished.
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.
42 cannot be simplified, so we are finished.

32. This can be divided which leaves the radical in the denominator
This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

33. This cannot be divided which leaves the radical in the denominator
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.
Reduce the fraction.

34. Simplify
= X
= Y3
= P2X3Y
= 2X2Y
= 5C4D10

35. Simplify = = = =

36. = = ? = =