The exponent is most often used in the power of monomials. SPECIAL FRACTION EXPONENT: The exponent is most often used in the power of monomials. Examples: Do you notice any other type of mathematical symbols that these special fraction exponents represent?

Radicals: Steps for Simplifying Square Roots Special Fraction Exponents, , are more commonly known as radicals in which the N value represents the root or index of the radical. Index Radical Symbol Radicals: Radicand Note: The square root or ½ exponent is the most common radical and does not need to have the index written. Steps for Simplifying Square Roots Prime Factorization: Factor the Radicand Completely Write the base of all perfect squares (PAIRS) outside of the radical as product Everything else (SINGLES) stays under the radical as a product.

[2] An EVEN index (n), cannot take negative radicands. Root Properties: [1] [2] An EVEN index (n), cannot take negative radicands. [3] An ODD index (n), can take both positive and negative radicands. Roots are the same sign as the radicand. General Notes: [1] 4 is the principal root [2] – 4 is the secondary root (opposite of the principal root) [3] ±4 indicates both primary and secondary roots

Simplifying Square Roots: Part 1 [C] [B] [C] [D] [E]

Simplifying Square Roots: Part 2 [B] [C] [A] [B] [D] [D]

Radicals Classwork: Additional Practice [2] [1] [3] [4] [5] [6] [8] [7] [9] [10] [11] [12]

Simplifying Any Root Same General Steps: Take out only groups of size n (the index) for the same base from the radical. These groups are called perfect roots. Example 1 a] b] c]

Example 2 A] B] [C] [D] [F] [E]

Applications Using Roots [A] The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula below, where L is the length of the pendulum in feet and g is the acceleration due to gravity. Find T for a 1.5 foot pendulum. Round to the nearest 100th and g = 32 ft/sec2. [B] The distance D in miles from an observer to the horizon over flat land or water can be estimated by the formula below, where h is the height in feet of observation. How far is the horizon for a person whose eyes are at 6 feet? Round to the nearest 100th.

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

Foil METHOD PRACITCE b] a] c] d]

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