Objective The student will be able to:

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Presentation transcript:

Objective The student will be able to: NOTES: Operations with Radical Expressions Objective The student will be able to: Simplify radical expressions involving addition and subtraction.

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.

How to Simplify Continued Example: Simplify First Method: Second Method: 4 12 2 2 4 3 2 2

Adding and Subtracting Radicals

Which are like radicals? 1. Simplify. Just like when adding variables, you can only combine LIKE radicals. 2. Simplify. Which are like radicals?

Simplify .

Perimeter = Add all of the sides 3. Find the perimeter of a rectangle whose length is and whose width is Perimeter = Add all of the sides

4. Simplify. Simplify each radical. * * * * * * Combine like radicals.

5. Simplify * * * * * *

Simplify .

Simplify .

Multiplying and Dividing Radicals

Multiplication Example Simplify: 1. Re-order 2. Multiply 3. Simplify Radical 4. Simplify 5. Simplify

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