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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

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What is a monomial? An expression that is a number, that may or may not include a variable. MONOMIALS NOT MONOMIALS

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Real Roots Real roots are the possible solutions to a number, raised to a power.

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**Vocabulary and Properties**

Radical sign index radicand

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**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 ENTER 3

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**Practice: Find each root**

Solutions: 22, 7, and ERR: NONREAL ANS Let’s take a closer look at this answer

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**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

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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.

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Let’s try some Simplify each expression. Use the absolute value symbols when needed.

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Solutions Simplify each expression. Use the absolute value symbols when needed.

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**Properties of Exponents – let’s review . . .**

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**NEGATIVE EXPONENT RULE**

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PRODUCT OR POWER RULE HAVE TO HAVE THE SAME BASE

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QUOTIENT OF POWER RULE HAVE TO HAVE THE SAME BASE

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POWER OF POWER RULE (x4)³

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POWER OF PRODUCT RULE (2x4)⁵

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**POWER OF A QUOTIENT RULE**

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POWER OF QUOTIENT 2 RULE

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**Fractional Exponents (Powers and Roots)**

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**RADICAL TO EXPONENT RULE**

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**RATIONAL EXPONENT RULE**

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