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? 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.

Properties of Exponents – let’s review . . .

NEGATIVE EXPONENT RULE

PRODUCT OR POWER RULE HAVE TO HAVE THE SAME BASE

QUOTIENT OF POWER RULE HAVE TO HAVE THE SAME BASE

POWER OF POWER RULE (x4)³

POWER OF PRODUCT RULE (2x4)⁵

POWER OF A QUOTIENT RULE

POWER OF QUOTIENT 2 RULE

Fractional Exponents (Powers and Roots)

RADICAL TO EXPONENT RULE

RATIONAL EXPONENT RULE