1. Lesson 2 – Simplifying Radicals

2. Essential Question
How can properties of exponents be used to write radical expressions in useful equivalent forms?

3. What is a Radical? index root radicand
We are familiar with taking square roots and even taking cubed roots, but you may not be as familiar with the elements of a radical.
index
root
radicand

4. What is a Radical?
An index in a radical tells you how many times you have to multiply the root times itself to get the radicand. When a radical is written without an index, there is an understood index of 2.
For example, in 81 , 81 is the radicand, 9 is the root, and the index is 2. You have to multiply 9 by itself twice to get the radicand (9•9 = 92 = 81).

5. Evaluating Radicals
Radicand:
Index:
Root: because
Root: because

6. Evaluating Radicals with the Calculator
For some of the more complex problems, you can use a calculator to help
Step 1: Type in the index
Step 2: Press MATH
Step 3: Choose 5
Step 4: Type in the radicand

7. Simplifying Radicals Investigation
Now you will have a chance to practice some on your own. Complete the three examples on the bottom of the page. Then move to the next side and read the introduction carefully. Your goal is to come up with methods and shortcuts to simplify the radicals.
Resource Manager: Ensure everyone is on the right page
Time Keeper: 10 minutes
Reader/Recorder: Read each question and the introduction
Spy Monitor: Check in with other groups or the key

8. Simplifying Radicals Find the Prime Factorization of the radicand
Any sets of “n” numbers (n=index) have one representative multiplied outside
Any remaining numbers no in a set are multiplied inside.

9. Examples
In your groups, complete the remaining problems

10. Laura’s Entryway The floor is 3 diagonals long and 2 diagonals wide.
Laura’s entry floor is made up of square tiles with 2-ft long sides
The diagonal of each tile is feet in length. Find the dimensions
of the floor, and then calculate the area.
The floor is 3 diagonals long and 2 diagonals wide.
Length: Width:

11. Multiplying Radicals
When written in radical form, it’s only possible to write two multiplied radicals as one if the index is the same.
Multiply the coefficients
Multiply the radicands
Simplify!

12. Examples
In your groups, complete the remaining problems

13. Adding & Subtracting Radicals
You can only add or subtract radicals that contain the same index and radicand.
Just like you don’t change the variable expression, you won’t change the radical expression.
Only add and subtract the coefficients.
ALWAYS SIMPLFY THE RADICAL FIRST!

14. Examples
In your groups, complete the remaining problems

15. Homework:
“Lesson 2 - Simplifying Radicals Homework”