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: 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.
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12. Ex. 4 G. H.

14. Ex. 5 A. B. C.
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15. Ex. 5 D. E.
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16. Ex. 5 F. G. 6 9