Objective The student will be able to:

1
ObjectiveThe student will be able to
NOTES Operations with Radical Expressions

• Simplify radical expressions involving addition
  and subtraction.

2
Reminder How to Simplify Radicals

• First Method
• -Rewrite radical as the product of the largest
  square and a number.
• -Separate and simplify.

Second Method -Create a factor tree by breaking
down each factor into prime numbers. -Create
pairs of prime numbers. -For each pair, one comes
outside of the radical. -Remainder is left
inside.
3
How to Simplify Continued

• Example Simplify
• First Method Second Method
• 4 12
• 2 2 4 3
• 2 2

4

• Adding and Subtracting
• Radicals

5
1. Simplify.

• Just like when adding variables, you can only
  combine LIKE radicals.

2. Simplify.
Which are like radicals?
6
Simplify

1. .
2. .
3. .
4. .

7
3. Find the perimeter of a rectangle whose
length is and whose width is

• Perimeter Add all of the sides

8
4. Simplify.

• Simplify each radical.

Combine like radicals.
9
5. Simplify






10
Simplify

1. .
2. .
3. .
4. .

11
Simplify

1. .
2. .
3. .
4. .

12
Multiplying and Dividing Radicals
13
Multiplication Example
Simplify
1. Re-order
2. Multiply
3. Simplify Radical
4. Simplify
5. Simplify
14
Division Example

• No Radicals in the Denominator! You must
  rationalize!
• 1. 2. 3.