1. Roots and Radical Expressions
6-1

2. Objective
To find the root.

3. Key Concept
If , a and b are both real numbers and n is a positive integer, then a is the nth root of b.
Radical Sign
Index
Radicand

4. Roots of Powers
For any real number a,
If n is odd
If n is even

5. Principle Root
There are two real roots of b. There is positive b, and negative b.

6. Finding all real roots What is the real cube root of 0.008?
What is the real fourth root of ?
Since is negative, there is no real fourth root.

7. What is the real cube root of ?
What is the real fourth root of ?

8. Finding Roots: What is the real-number root?
So,
So,

9. Finding Roots: What is the real-number root?
There is no real root because there is no real number whose fourth power is -1.

10. Simplifying Radical Expressions

11. Simplify Radical Expressions:
Questions Answers

12. STEM
The voltage V of an audio systems speakers can be represented by , where P is the power of the speaker. An engineer wants to design a speaker with watts of power. What will the voltage be?

13. Definition of i
The imaginary number, i, was invented so we can solve equations like:
Remember, it’s Not a Real Number!
It’s an Imaginary Number!

14. You can find any power of i
Properties of i
They repeat the first 4!
You can find any power of i

15. Simplify Memorize the first 4 powers of i: Divide the exponent by 4
Your answer is i with the remainder as it’s exponent.
Memorize the first 4 powers of i:

16. T.O.O. Simplify 1) 2) 4) 3)

17. Simplify 1) 2) Not a real number, but now have new definition
Put the i in front of radical!
i after integer
Don’t write:

18. Homework
Pg 364 # Odd, 30, ALL