1. Simplifying Radical Expressions

2. Product Property of Radicals
For any numbers a and b where and ,

3. Product Property of Radicals Examples

4. Examples:

5. Examples:

6. Quotient Property of Radicals
For any numbers a and b where and ,

7. Examples:

8. Examples:

9. Rationalizing the denominator
Rationalizing the denominator means to remove any radicals from the denominator.
Ex: Simplify

10. Simplest Radical Form No perfect nth power factors other than 1.
No fractions in the radicand.
No radicals in the denominator.

11. Examples:

12. Examples:

13. Reverse of the Distributive Property
Adding radicals
We can only combine terms with radicals
if we have like radicals
Reverse of the Distributive Property

14. Examples:

15. Examples:

16. Multiplying radicals - Distributive Property

17. Multiplying radicals - FOIL

18. Examples: F O I L

19. Examples: F O I L

20. where a, b, c, d are rational numbers.
Conjugates
Binomials of the form
where a, b, c, d are rational numbers.

21. The product of conjugates is a rational number
The product of conjugates is a rational number. Therefore, we can rationalize denominator of a fraction by multiplying by its conjugate.

22. Examples:

23. Examples: