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.

Ex. 1

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.

Ex. 2

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.

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

Ex. 3

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

Ex. 4 D. E. F. ________________________ 10

Ex. 4 G. H.

Ex. 5 A. B. C. ________________________ ________________________

Ex. 5 D. E. ________________________

Ex. 5 F. G. 6 9