1. Radicals are in simplest form when:
No factor of the radicand is a perfect square other than 1.
The radicand contains no fractions
No radical appears in the denominator of a fraction

2. Perfect Squares 64
225 1 81
256 4
100
289 9
121 16
324
144 25
400
169 36 49
196
625

3. Multiplication property of square roots:
Division property of square roots:

4. Simplify
= 2
= 4
= 5
This is a piece of cake!
= 10
= 12

5. To Simplify Radicals you must make sure that you do not leave any perfect square factors under the radical sign. *Think of the factors of the radicand that are perfect squares.
Perfect Square Factor * Other Factor =
LEAVE IN RADICAL FORM =

6. Simplify = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = =

7. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

8. If you cannot think of any factors that are perfect squares – prime factor the radicand to see if you have any repeated factors
EX: 20 10
2 5

9. You can simplify radicals that have variables TOO!= = = = =

12. Radicals are in simplest form when:
No factor of the radicand is a perfect square other than 1.
The radicand contains no fractions
No radical appears in the denominator of a fraction

13. REMEMBER THE PRODUCT PROPERTY OF SQUARE ROOTS:
Multiply Square Roots
REMEMBER THE PRODUCT PROPERTY OF SQUARE ROOTS: OR

14. 4 Multiply Square Roots To multiply square roots –
you multiply the radicands together then simplify
EX: * = = 4
Simplify =

15. Try These : * * *

16. Let’s try some more:

17. Multiply Square Roots Multiply the coefficients Multiply the radicands
Simplify the radical.

18. Multiply & Simplify Practice

19. Homework Practice 1. 2. 3. 4. 5.

20. Radicals are in simplest form when:
No factor of the radicand is a perfect square other than 1.
The radicand contains no fractions
No radical appears in the denominator of a fraction

21. Division property of square roots:

22. To simplify a radicand that contains a fraction –
first put a separate radical in the numerator and denominator
Then simplify

23. Try These :
Simplify:

24. If we have a radical left in the denominator then we must rationalize the denominator:
Since we cannot leave a radical in the denominator we must multiply both the numerator and the denominator by this radical to rationalize = = = = *

25. Hint – you will need to rationalize the denominator
Simplify:
Hint – you will need to rationalize the denominator A.
B. 4  C.
D. 16 

26. Simplify Radicals 1) 2) 3) 4)

27. Simplify some more: 5) 6) 7) 8)

28. Review writing in simplest radical form:1) 2) 3) 4) 5) 6)

29. Review writing in simplest radical form:7) 8) 9)

30. Which of the following is not a condition
of a radical expression in simplest form? 
A. No radicals appear in the numerator of a fraction. 
B. No radicands have perfect square factors other than 1. 
C. No radicals appear in the denominator of a fraction. 
D. No radicands contain fractions.

31. Adding and subtracting radical expressions
You can only add or subtract radicals together if they are like radicals – the radicands MUST be the same