1. List of Some Perfect Squares

2. Example:
Check using a calculator!

3. Simplify. To simplify the number by hand
This wont help because neither 6 nor 3 are perfect squares!
To simplify the number by hand
must have a perfect square factor.
No perfect
square factors
Can’t be
simplified

4. Notice all solutions are using factors that are perfect squares!1) 4) 2) 5) 3) 6)

5. Simplify.
Perfect square

6. Simplify each irrational root.1) 4)
Already
Simplified 2) 5) 3) 6)

7. Radicals with Variables
To simplify radicals with variables: divide even exponents by 2; for odd exponents, pull out the largest even exponent, take the square root of that, and leave the remainder under the radical.

8. Radicals with Variables
Ex. 10 Even
Radicals with Variables
Answer : X
Answer: P^2 X^3 Y
Answer: 5 C^4 D^5

9. Radicals with Variables
Ex. 11 Odd
Radicals with Variables

10. + Combine Like Radicals
Miller
Miller
To combine radicals: combine the coefficients of like radicals. They must have the same last name.

11. Ex. 3 Simplify
Your Turn

12. Ex. 4
Simplify, then combine.

13. Ex. 5
Simplify, then combine.

14. Example The greatest perfect square factor of 96a4b is 16a4.
Use the product rule of square roots to separate the factors into two radicals.
Find the square root of 16a4 and leave 6b in the radical.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

15. Example Solution The greatest perfect square factor of 32x5 is 16x4.
Use the product rule of square roots to separate the factors into two radicals.
Find the square root of 16x4 and leave 2x in the radical.

16. Multiply Radicals *
To multiply radicals: multiply everything, then simplify.

17. Dividing Radicals
To divide radicals: reduce or divide what you can and rationalize the denominator. A square root CANNOT be in the denominator.

18. 7.5 – Rationalizing the Denominator of Radicals Expressions
Radical expressions, at times, are easier to work with if the denominator does not contain a radical. The process to clear the denominator of all radical is referred to as rationalizing the denominator

19. 7.5 – Rationalizing the Denominator of Radicals Expressions

20. 7.5 – Rationalizing the Denominator of Radicals Expressions

21. 7.5 – Rationalizing the Denominator of Radicals Expressions
If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required.
Review:
(x + 3)(x – 3) 
x2 – 3x + 3x – 9 
x2 – 9
(x + 7)(x – 7) 
x2 – 7x + 7x – 49 
x2 – 49

22. 7.5 – Rationalizing the Denominator of Radicals Expressions
If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required.
conjugate

23. 7.5 – Rationalizing the Denominator of Radicals Expressions
conjugate

24. 7.5 – Rationalizing the Denominator of Radicals Expressions
conjugate