Simplifying Radicals Index Radical Radicand Note With square

Simplifying Radicals Index Radical Radicand Note: With square roots the index is not written Steps for Simplifying Square Roots 1. Factor the Radicand Completely or until you find a perfect root 2. Take out perfect roots (look for pairs) 3. Everything else (no pairs) stays under the radical

Root Properties: [1] [2] If you have an even index, you cannot take roots of negative numbers. Roots will be positive. [3] If you have an odd index, you can take the roots of both positive and negative numbers. Roots may be both positive and negative

Example 3 Simplify Sums / Differences • Find common radicand • Combine like terms a] b]

ADD and SUBTRACT radical expressions 1) Find common radicand (simplify) 2) Combine like terms (outsides only) a] b] [c] d] e] f]

Simplifying Radicals: “Inside to Inside and Outside to Outside” 1. Multiply radicand by radicand 2. If it’s not underneath the radical then do not multiply, write together (ex: ) Multiplying Radical Expressions: Distribute and FOIL [A] [B] [C] [D]

Foil METHOD PRACITCE a] c] b] d]

Conjugate: Rationalizing: Value that is multiplied to a radical expression That clears the radical. Multiplying the denominator of a fraction by its conjugate.

Example 3 Rationalizing Cube Roots [A] [B] [C] [D]

Example 4 [A] Tougher Rationalizing [B]

Simplifying Radicals [1] [2] [7] [8] [3] [4] [9] [10] [5] [6] [11] [12]