1. 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?

2. 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.

3. [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

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

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

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

7. 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]

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

9. 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.

10. 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]

11. Foil METHOD PRACITCE b] a] c] d]

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