1. Introduction to Radicals
Radical Expressions
Finding a root of a number is the inverse operation of raising a number to a power.
radical sign
index
radicand
This symbol is the radical or the radical sign
The expression under the radical sign is the radicand.
The index defines the root to be taken.

2. Introduction to Radicals
Square Roots
A square root of any positive number has two roots – one is positive and the other is negative.
If a is a positive number, then
is the positive square root of a and
is the negative square root of a.
Examples:
non-real #

3. Introduction to Radicals
What does the following symbol represent?
The symbol represents the positive or principal root of a number.
What is the radicand of the expression ?
5xy

4. Introduction to Radicals
What does the following symbol represent?
The symbol represents the negative root of a number.
What is the index of the expression ? 3

5. Introduction to Radicals
Cube Roots
A cube root of any positive number is positive.
A cube root of any negative number is negative.
Examples:

6. Introduction to Radicals
nth Roots
An nth root of any number a is a number whose nth power is a.
Examples:

7. Introduction to Radicals
nth Roots
An nth root of any number a is a number whose nth power is a.
Examples:
Non-real number
Non-real number

8. Introduction to Radicals
Radicals with Variables
Examples:

9. Simplifying Radicals using the Product Rule
Product Rule for Square Roots
Examples:

10. Simplifying Radicals using the Quotient Rule
Quotient Rule for Square Roots
Examples:

11. Simplifying Radicals Containing Variables
Examples:

12. Simplifying Cube Roots
Simplifying Radicals
Simplifying Cube Roots
Examples:

13. Simplifying Radicals
Examples:

14. Simplifying Radicals
Examples:

15. Day One Stop Here

16. Adding and Subtracting Radicals
Review and Examples:

17. Adding and Subtracting Radicals
Simplifying Radicals Prior to Adding or Subtracting

18. Adding and Subtracting Radicals
Simplifying Radicals Prior to Adding or Subtracting