1. Radicals Simplify radical expressions using the properties of radicals
Multiplying and dividing radical expressions using the properties of radicals
Adding and subtracting radical expressions using the properties of radicals

2. Radical Notation
n is called the index number
a is called the radicand

3. Properties of Radicals

4. Simplifying Radicals
The radicand has no factor raised to a power greater than or equal to the index number
The radicand has no fractions
No denominator contains a radical
Exponents in the radicand and the index of the radical have no common factor
All indicated operations have been performed

6. Simplify the following expressions

7. Simplifying Radicals If there is no index #, it is understood to be 2
When simplifying radicals use perfect squares, cubes, etc.
Use factor trees to break a number into its prime factors
Apply the properties of radicals and exponents

8. Simplify each of the following radicals
Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers.

9. Simplify each of the following radicals
Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers.

10. Rewrite each of the following as a single number under the radical sign

11. Multiplying Radicals Radicals must have the same index number
Multiply outsides and insides together
Add exponents when multiplying
Simplify your expression
Combine all like terms

12. Simplify each of the following radicals
Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers.

13. Dividing Radicals No radicals in the denominator
No fractions under the radical sign
Apply the properties of radicals and exponents

14. Simplify each of the following radicals
Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers and that no denominators are zero.

15. Simplify each of the following radicals
Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers and that no denominators are zero.

16. Add/Subtract Radicals
Simplify each radical expression
Radicals must have the same index number and same radicand
Add the outside numbers together and the radicand remains the same

17. Simplify each of the following radicals

18. Mult/Dividing Radicals
Simplify each of the following radicals

19. Mult/Dividing Radicals
Multiply using fractional exponents and the properties of exponents. Write your answer in radical form and simplify.
Multiply by changing the radicals to a common index and simplify.