1. Introduction to Radicals

2. This symbol is the radical or the radical sign
Radical Expressions
Finding a root of a number is the inverse operation of raising a number to a power.
radical sign
index
radicand
This symbol is the radical or the radical sign
The expression under the radical sign is the radicand.
The index defines the root to be taken.

3. Square Roots
A square root of any positive number has two roots – one is positive and the other is negative.
If a is a positive number, then
is the positive (principal) square root of a and
is the negative square root of a.
Examples:
non-real #

4. What does the following symbol represent?
The symbol represents the positive or principal root of a number.
What is the radicand of the expression ?
5xy

5. What does the following symbol represent?
The symbol represents the negative root of a number.
What is the index of the expression ? 3

6. 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, ...

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

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

9. Simplifying Radicals

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

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

12. Simplify .

13. Simplify
3x6
3x18
9x6
9x18

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

15. Simplify each expression

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

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

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

19. Simplify each expression

20. Simplify each expression

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

22. Multiply and then simplify

24. 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

25. That was easy!

26. 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.

27. 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.

28. 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.

29. Simplify
= X
= Y3
= P2X3Y
= 2X2Y
= 5C4D5

30. Simplify = = = =

31. worksheet --- Non-Perfect Squares
Classwork:
Packet in Yellow Folder under the desk nd page
Homework:
worksheet --- Non-Perfect Squares
(#1-12)