1. Simplifying Radical Expressions

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

3. Product Property of Radicals Examples

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

5. Examples:

6. Examples:

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

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

9. Examples:

10. Examples:

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

12. Examples:

13. Examples:

14. Multiplying radicals - Distributive Property

15. Multiplying radicals - FOIL

16. Examples:

17. Examples:

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

19. 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.

20. Examples:

21. Examples: