1. Warm-Up #5 Find the product of ab. Let a= 1 2 𝑎𝑛𝑑 𝑏= 25 36 .
Simplify 91
Estimate: What is 17

2. Homework
Advanced: Simplifying Radical Worksheet Page 1. #1-6 Page 2. #1-6 Regular: Simplifying Radical Worksheet Page 1. #1-4 Page 2. #1-4

3. Introduction to Radicals

4. Principal Square Roots
The principal (positive) square root is noted as
The negative square root is noted as

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

6. Simplify
= 4 or -4
= 5 or -5
= 10 or -10
= 12 or -12

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

8. Cube Roots
The cube root of a real number a
Example:

9. 15.1 – Introduction to Radicals
Cube Roots
A cube root of any positive number is positive.
A cube root of any negative number is negative.
Examples:

10. Cube Roots
Example

11. Simplifying Radicals

12. Product Rule for Radicals
If and are real numbers,

13. Simplifying Radicals Example
Simplify the following radical expressions.
No perfect square factor, so the radical is already simplified.

14. Simplifying Radicals Example
Simplify the following radical expressions.

15. Quotient Rule for Radicals
If and are real numbers,

16. Simplifying Radicals Example
Simplify the following radical expressions.

17. Adding and Subtracting Radicals

18. Sums and Differences
Rules in the previous section allowed us to split radicals that had a radicand which was a product or a quotient.
We can NOT split sums or differences.

19. Like Radicals What is combining “like terms”?
Similarly, we can work with the concept of “like” radicals to combine radicals with the same radicand.

20. Adding and Subtracting Radical Expressions
Example
Can not simplify
Can not simplify

21. Adding and Subtracting Radical Expressions
Example
Simplify the following radical expression.

22. Adding and Subtracting Radical Expressions
Example
Simplify the following radical expression.

23. Adding and Subtracting Radical Expressions
Example
Simplify the following radical expression. Assume that variables represent positive real numbers.

24. Multiplying and Dividing Radicals

25. Multiplying and Dividing Radical Expressions
If and are real numbers,

26. Multiplying and Dividing Radical Expressions
Example
Simplify the following radical expressions.

27. Rationalizing the Denominator
If we rewrite the expression so that there is no radical in the denominator, it is called rationalizing the denominator.
Rationalizing the denominator is the process of eliminating the radical in the denominator.

28. Rationalizing the Denominator
Example
Rationalize the denominator.

29. Conjugates
Many rational quotients have a sum or difference of terms in a denominator, rather than a single radical.
need to multiply by the conjugate of the denominator
The conjugate uses the same terms, but the opposite operation (+ or ).

31. Rationalizing the Denominator
Example
Rationalize the denominator.