12.1 Operations with Radicals

1. 12.1 Operations with Radicals Objectives: Identify or estimate square roots. Define and write square roots in simplest radical form. Perform mathematical operations with radicals. Standard Addressed: 2.1.11.A Use operations.

3. Ex. 1

4. Simplifying Radicals and Radical Expressions In order to add or subtract expressions that contain radicals, radicands must be equal. Terms that contain , for example, can be added by applying the Distributive Property.

5. Ex. 2

7. Radical expressions that are simplified n are easier to manipulate algebraically. A square-root expression is in simplest radical form when all the following conditions are met: • No factor of the radicand is a perfect square other than 1. • The radicand contains no fractions. • No radical appears in the denominator of a fraction.

8. Perfect Square > 1  Fraction  Radical in the Denominator  Simplest Radical Form 

9. Ex. 3

10. Ex. 4 Simplify. • A. • B. • C. 75 ________________________ ________________________

11. Ex. 4 • D. • E. • F. ________________________ 10

12. Ex. 4 • G. • H.

14. Ex. 5 • A. • B. • C. ________________________ ________________________

15. Ex. 5 • D. • E. ________________________

16. Ex. 5 • F. • G. 6 9