1. Binomial Radical Expressions
7.3
Adding, Subtracting, Multiplying and Dividing
Binomial Radical Expressions

2. Adding Radical Expressions
Use the same concept as that of adding or subtracting like variables.
Example: x + 2x + 5
*Have to have like Terms to Add/Subtract*

3. Like Radicals are radical expressions that have the same index and the same radicand.

4. Like Radicals Unlike Radicals

5. Examples:
1. 2.

7. Always simplify radicals before combining!

9. Multiplying Radical Expressions
When multiplying radicals, one must multiply the numbers OUTSIDE (O) the radicals AND then multiply the numbers INSIDE (I) the radicals.

10. Dividing Radical Expressions
When dividing radicals, one must divide the numbers OUTSIDE (O) the radicals AND then divide the numbers INSIDE (I) the radicals. Remember to rationalize the denominator if needed!

11. Examples:

12. Multiplying Binomials
To multiply, USE FOIL! Example 1:

13. 2. 3.

14. Dividing Binomial Radicals
To divide, Rationalize the denominator! (a + b)( a - b) = a2 – b2 These are called conjugates. They make radicals disappear!

15. Rationalize the denominator1.

16. Rationalize the denominator:2.

17. Simplify:
1. 2.

18. 3. 4.

19. Examples: 1.