1. Adding, Subtracting, and Multiplying Radical Expressions
10.4
Adding, Subtracting, and Multiplying Radical Expressions
1. Add or subtract like radicals.
2. Use the distributive property in expressions containing radicals.
3. Simplify radical expressions that contain mixed operations.

2. Simplify. 1) 2) 3)

3. Adding Radical Expressions
Like radicals: Radical expressions with identical radicands and indices (roots).
Adding Like Radicals
Add or subtract the coefficients and leave the radical parts the same.

4. Add:

5. Add:
4∙6
9∙6

6. Add:
9∙3
25∙3

7. Add:
49∙2
64∙2

8. Add:

9. Copyright © 2011 Pearson Education, Inc.
Simplify. a) b) c) d)
Copyright © 2011 Pearson Education, Inc.

10. Copyright © 2011 Pearson Education, Inc.
Simplify. a) b) c) d)
Copyright © 2011 Pearson Education, Inc.

11. Simplify:
Distributive Property
If the indexes are the same, multiply the radicands.

12. Simplify:
Foil
Multiply coefficients.
Multiply radicals.

13. Simplify:
Rewrite and Foil!
Multiply coefficients.
Multiply radicals.

14. Simplify:
Conjugates

15. To multiply radicals, the index must be the same.
If the index is the same, multiply the coefficients together and multiply the radicands together.
To add radicals, the radicals must be the same (same index and same radicand).
Add the coefficients together and keep the same radical.

16. Simplify:
49∙2

17. Simplify:

18. Simplify:
27∙3

19. Simplify:

20. Copyright © 2011 Pearson Education, Inc.
Multiply. a) b) c) d)
Copyright © 2011 Pearson Education, Inc.

21. Copyright © 2011 Pearson Education, Inc.
Multiply. a) b) c) d)
Copyright © 2011 Pearson Education, Inc.