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.
Simplify. 1) 2) 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.
Add:
Add: 4∙6 9∙6
Add: 9∙3 25∙3
Add: 49∙2 64∙2
Add:
Copyright © 2011 Pearson Education, Inc. Simplify. a) b) c) d) Copyright © 2011 Pearson Education, Inc.
Copyright © 2011 Pearson Education, Inc. Simplify. a) b) c) d) Copyright © 2011 Pearson Education, Inc.
Simplify: Distributive Property If the indexes are the same, multiply the radicands.
Simplify: Foil Multiply coefficients. Multiply radicals.
Simplify: Rewrite and Foil! Multiply coefficients. Multiply radicals.
Simplify: Conjugates
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.
Simplify: 49∙2
Simplify:
Simplify: 27∙3
Simplify:
Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) Copyright © 2011 Pearson Education, Inc.
Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) Copyright © 2011 Pearson Education, Inc.