This document discusses dividing radicals and rationalizing radicals. It provides examples of rationalizing radicals by applying the law of radicals to make the denominator free of radicals. Examples of dividing radicals with the same index are also shown. The steps for dividing radicals are to divide the radicands and rationalize if needed to remove radicals from the denominator. An activity is included where students work in groups to solve radical expressions and present their work.

1. Division of
Radicals

2. Objectives
Rationalize a given
radical
Divide radicals with the
same index

3. Remember:
There should be
NO radicals on the
denominator.

4. Rationalization
Process of making the
denominator free from radicals

5. Recall:
Law of Radical #1
𝑛
𝑎𝑛 = 𝑎
-This applies to the process of
rationalization

6. Example 1:
5
Solution:
5 ( 5)= 52 = 5

7. Example 2:
3
7
Solution:
3
7 (
3
72)=
3
73 = 7

8. Activity:
Table
Completion
Given Multiplier Product
2 2 2
4
3 4
33 3
3
𝑚2
3
𝑚 m
𝑥𝑦 𝑥𝑦 xy
3
𝑎2𝑏
3
𝑎𝑏2 ab

9. Objectives
Rationalize a given
radical
Divide radicals with the
same index

10. How to
divide
radicals?
Remember: Law of Radical #3-
𝑛
𝑎
𝑛
𝑏
=
𝑛 𝑎
𝑏
Dividing radicals with the same index
-Divide the given radicand
-Rationalize if necessary

11. How to
divide
radicals?
Example #1:
3
16
3
2
3
16
3
2
=
3 16
2
Divide
=
3
8 Simplify
= 2 Answer

12. How to
divide
radicals?
Example #2:
3
5
3
2
3
5
3
2
∗
3
22
3
22
Rationalize
=
3
5
3
4
3
23
Simplify
=
3
20
2
Answer

13. Group
Activity
1. Each group will be given a
radical expression to solve.
2.5 minutes will be given to talk
about the solution.
3. The group will present the
solution on the board in a
maximum of 2 minutes per
group. (Make sure to start the
presentation with a yell)

14. Objectives
Rationalize a given
radical
Divide radicals with the
same index

15. Seat
Work
Divide the following radical
expressions and rationalize if
necessary:
1.
300
3
2.
3
6
3
5

16. Remember
Radicals can be divided if the
index are the same.
If the quotient appears to have a
radical on the denominator,
rationalization is needed.
Rationalization is applied to
make the denominator free from
radicals.