1. 7. Roots and Radical Expressions

2. 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

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

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

5. Vocabulary and Properties
Radical sign
index
radicand

6. 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

7. Practice: Find each root
Solutions: 22, 7, and
ERR: NONREAL ANS
Let’s take a closer look at this answer

8. 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

9. 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.

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

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

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

13. NEGATIVE EXPONENT RULE

14. PRODUCT OR POWER RULE
HAVE TO HAVE THE SAME BASE

15. QUOTIENT OF POWER RULE
HAVE TO HAVE THE SAME BASE

16. POWER OF POWER RULE
(x4)³

17. POWER OF PRODUCT RULE
(2x4)⁵

18. POWER OF A QUOTIENT RULE

19. POWER OF QUOTIENT 2 RULE

20. Fractional Exponents (Powers and Roots)

21. RADICAL TO EXPONENT RULE

22. RATIONAL EXPONENT RULE