1. 6.2 – Simplified Form for Radicals
Product Rule for Square Roots
Examples:

2. 6.2 – Simplified Form for Radicals
Quotient Rule for Square Roots
Examples:

3. 6.2 – Simplified Form for Radicals

4. 6.2 – Simplified Form for Radicals
Rationalizing the Denominator
Radical expressions, at times, are easier to work with if the denominator does not contain a radical. The process to clear the denominator of all radicals is referred to as rationalizing the denominator

5. 6.2 – Simplified Form for Radicals
Examples:

6. 6.2 – Simplified Form for Radicals
Examples:

7. 6.2 – Simplified Form for Radicals
Theorem:
If “a” is a real number, then 𝑎 2 = 𝑎 .
Examples:
40 𝑥 2
𝑥 2 −16𝑥+64
18𝑥 3 −9 𝑥 2
4∙10 𝑥 2
𝑥−8 2
9𝑥 2 2𝑥−1
2 𝑥 10
𝑥−8 3 𝑥
2𝑥−1

8. 6.3 - Addition and Subtraction of Radical Expressions
Review and Examples:

9. 6.3 - Addition and Subtraction of Radical Expressions
Simplifying Radicals Prior to Adding or Subtracting

10. 6.3 - Addition and Subtraction of Radical Expressions
Simplifying Radicals Prior to Adding or Subtracting

11. 6.3 - Addition and Subtraction of Radical Expressions
Simplifying Radicals Prior to Adding or Subtracting

12. 6.3 - Addition and Subtraction of Radical Expressions
Examples:

13. 6.3 - Addition and Subtraction of Radical Expressions
Examples:

14. 6.3 - Addition and Subtraction of Radical Expressions
A Challenging Example
2 𝑥 2 𝑦 4 𝑧
2 𝑥 2 𝑧 3
𝑥 𝑦 𝑧 3 5
2 𝑥 2 𝑧 3
𝑥 𝑦 𝑧 18 5

15. 6.4 –Multiplication and Division of Radical Expressions
Examples:

16. 6.4 –Multiplication and Division of Radical Expressions
Examples:
𝑥− 3𝑥 + 5𝑥 − 15

17. 6.4 –Multiplication and Division of Radical Expressions
Examples:

18. 6.4 –Multiplication and Division of Radical Expressions
Review:
(x + 3)(x – 3) 
x2 – 3x + 3x – 9 
x2 – 9
𝑥 𝑥 −3
𝑥 2 −3 𝑥 +3 𝑥 −9
𝑥−9

19. 6.4 –Multiplication and Division of Radical Expressions
If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required in order to rationalize the denominator.
conjugate

20. 6.4 –Multiplication and Division of Radical Expressions
Example:

21. 6.4 –Multiplication and Division of Radical Expressions
Example: