1. Simplifying Radicals
Section 10-2 Part 1

2. Goals Goal Rubric To simplify radicals involving products.
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more advanced problems.
Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary
Radical Expression

4. Definitions
Radical Expression - an expression that contains a radical sign
There are many different types of radical expressions, but in this course, you will only study radical expressions that contain square roots.
Examples:
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.

5. Simplest Form

6. Simplest Form Simplified Not Simplified Radicand contains a fraction.
Radicand contains a perfect square factor.
Radical appears in the denominator of a fraction.

7. Multiplying Radicals

8. Example: Multiplying Radicals

9. Your Turn:

10. Simplifying Radicals Removing Perfect-Square factors
The radicand has no perfect-square factors other than 1.
Simplifying Radicals Removing Perfect-Square factors

11. These numbers are called the Perfect Squares.
The terms of the following sequence:
1, 4, 9, 16, 25, 36, 49, 64, 81…
12,22,32,42, 52 , 62 , 72 , 82 , 92…
These numbers are called the Perfect Squares.

12. Removing Perfect-Square Factors
Like the number 3/6, is not in its simplest form. Also, the process of simplification for both numbers involves factors.
Factoring out a perfect square.

13. Procedure: Removing Perfect-Square Factors
1. Find the largest perfect square that is a factor of the radicand.
2. Rewrite the radicand as
a product of its largest
square and some other
number.
3. Take the square root of
the perfect square. Write
it as a product.
4. Leave the number that
you didn’t take the
square root of under
the radical sign.
Perfect squares:
1, 4 , 9, 16, 25, 36,
49, 64, 81, 100,...

14. Example: Simplify. Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.

15. Examples:

16. Your Turn: Simplify. Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.

17. Your Turn:
Simplify.

18. Removing Variable Factors
Example: Simplify the following:
To simplify a variable with an exponent, write the product of the form where n is the largest possible even exponent.
As a general rule, divide the exponent by two. 15 ÷ 2= 7 with remainder 1. The remainder stays in the radical.

19. Example: Removing Variable Factors
Simplify.
Product Property of Square Roots.
Product Property of Square Roots.

20. Example: Removing Variable Factors
Simplify.
Factor the radicand using perfect squares.
Product Property of Square Roots.
Simplify.

21. Your Turn: Simplify. Product Property of Square Roots.

22. Your Turn: = 15x √ 225x2 = 5y3 √ 25y6 = 6xy2 √2y √ 72x2y5 = 7m√2m
12.1 and Operations with Radicals
√ 225x2
= 15x
= 5y3
√ 25y6
= 6xy2 √2y
√ 72x2y5
√ 98m3
= 7m√2m
√ 27x4
= 3x2√3

23. Multiplying Radicals Expressions
To multiply radicals …multiply the inside by the inside
and the outside by the outside.
Then simplify.

24. Your Turn: It may be easier to simplify the radicals first. 16 5 16 2

25. Example: Multiply Radical Expressions
Multiply and simplify.
Multiply the coefficients.
Multiply the radicals.

26. Example:
Multiply and simplify.

27. Your Turn:
Multiply and simplify.

28. Your Turn:
Multiply and simplify.

29. Multiply
Multiply and simplify.

30. Assignment
10-2 Pt 1 Exercises Pg. 613: #6 – 30 even