1. Warm Up
Identify the perfect square in each set.
Write each number as a product of prime numbers.
List all of the factor pairs for the number.
9. 20
10. 27
11. 98 25 81
256
196
1 & 20; 2 & 10; 4 & 5
1 & 27; 3 & 9
1 & 98; 2 & 49; 7 & 14
1 & 128; 2 & 64; 4 & 32; 8 & 16

2. Simplifying Radical Expressions
Simplest form
Product Property
Quotient Property

3. Objective Vocabulary Simplify radical expressions. radical expression
radicand

4. An expression that contains a radical sign is a radical expression
An expression that contains a radical sign is a radical expression. There are many different types of radical expressions, you will only study radical expressions that contain square roots.
Examples of radical expressions:
The expression under a radical sign is the radicand. A radicand may contain numbers, variables, or both. It may contain one term or more than one term.

6. Remember that positive numbers have two square roots, one positive and one negative. However, indicates a nonnegative square root. When you simplify, be sure that your answer is not negative. To simplify you should write because you do not know whether x is positive or negative.

7. Simplifying Square-Root Expressions
Simplify each expression. A. B.

8. Simplify each expression.
Try This!
Simplify each expression. a. b. c.

10. Using the Product Property of Square Roots
Simplify. All variables represent nonnegative numbers.
Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.

11. Using the Product Property of Square Roots
Simplify. All variables represent nonnegative numbers.
Product Property of Square Roots.
Product Property of Square Roots.
Since x is nonnegative,

12. Simplify. All variables represent nonnegative numbers.
Try This!
Simplify. All variables represent nonnegative numbers.
Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.

13. Simplify. All variables represent nonnegative numbers.
Try This!
Simplify. All variables represent nonnegative numbers.
Product Property of Square Roots.
Product Property of Square Roots.
Since y is nonnegative,

14. Simplify. All variables represent nonnegative numbers.
Try This!
Simplify. All variables represent nonnegative numbers.
Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.

16. Using the Quotient Property of Square Roots
Simplify. All variables represent nonnegative numbers. A. B.
Simplify.
Quotient Property of Square Roots.
Quotient Property of Square Roots.
Simplify.
Simplify.

17. Simplify. All variables represent nonnegative numbers.
Try This!
Simplify. All variables represent nonnegative numbers. a. b.
Quotient Property of Square Roots.
Simplify.
Quotient Property of Square Roots.
Simplify.
Simplify.

18. Simplify. All variables represent nonnegative numbers.
Try This!
Simplify. All variables represent nonnegative numbers.
Quotient Property of Square Roots.
Factor the radicand using perfect squares.
Simplify.

19. Using the Product and Quotient Properties Together
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Product Property.
Write 108 as 36(3).
Simplify.

20. Using the Product and Quotient Properties Together
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Product Property.
Simplify.

21. Simplify. All variables represent nonnegative numbers.
Try This!
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Product Property.
Write 20 as 4(5).
Simplify.

22. Simplify. All variables represent nonnegative numbers.
Try This!
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Product Property.
Write as as
Simplify.

23. Simplify. All variables represent nonnegative numbers.
Try This!
Simplify. All variables represent nonnegative numbers.
Quotient Property.
Simplify.

24. Simplify each expression.
Lesson Quiz:
Simplify each expression. 1. 6 2. 5
Simplify. All variables represent nonnegative numbers. 3. 4. 5. 6.