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7. Roots and Radical Expressions. In this chapter, you will learn:. What a polynomial is Add/subtract/multiply/divide polynomials Simplify radicals, exponents Solving equations with exponents and radicals Complex numbers Conjugates. What is a monomial?.

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## 7. Roots and Radical Expressions

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**In this chapter, you will learn:**What a polynomial is Add/subtract/multiply/divide polynomials Simplify radicals, exponents Solving equations with exponents and radicals Complex numbers Conjugates**What is a monomial?**An expression that is a number, that may or may not include a variable. MONOMIALS NOT MONOMIALS**Real Roots**• Real roots are the possible solutions to a number, raised to a power.**Vocabulary and Properties**Radical sign index radicand**How to find the root (other than a square root), using a**graphing calculator 1. Input the root you are going to take (for example, if you are taking the third root of a number, start with the 3). 2. Press MATH and select option 5 3. Enter the value you are taking the root of. Ex: 4 MATH 5 81 ENTER 3**Practice: Find each root**Solutions: 22, 7, and ERR: NONREAL ANS Let’s take a closer look at this answer**Properties and Notation:**Why? We want to make sure that the root is always positive when the index is an even number When n is an even number**Note: Absolute value symbols ensure that the root is**positive when x is negative. They are not needed for y because y2 is never negative. Notice that the index is an odd number here . . . Absolute value symbols must not be used here. If x is negative, then the radicand is negative and the root must also be negative.**Let’s try some**Simplify each expression. Use the absolute value symbols when needed.**Solutions**Simplify each expression. Use the absolute value symbols when needed.**PRODUCT OR POWERRULE**HAVE TO HAVE THESAME BASE**QUOTIENT OF POWERRULE**HAVE TO HAVE THESAME BASE**POWER OF POWERRULE**(x4)³**POWER OF PRODUCTRULE**(2x4)⁵**Fractional Exponents (Powers and Roots)**“Power” “Root”

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