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4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Radical OperationsDay 1

N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. (i.e., simplify and/or use the operations of addition, subtraction, and multiplication, with radicals within expressions limited to square roots). 

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

What am I learning today?

How to simplify and multiply radical expressions

How will I show that I learned it?Multiply 2 square‐root expressions, including 

variables

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

4

Index

RadicalRadicand

Vocabulary:

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Properties of Radicals:Product Property:

We use this to both simplify and multiply radicals.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Simplifying Radicals (Square Roots):Step 1: Factor the radicand into its prime factors.Step 2: Group same factors in groups of 2.Step 3: For every group you have, you have a perfect root and can move that factor outside the radical.Step 4: Multiply your outside factors together and your inside factors together to simplify your radical.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Example A.

Example B.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Example C.

Example D.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Example E.

Example F.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Multiplying Radicals:Step 1: Factor radicands.Step 2: Multiply coefficients and combine factors of radicands under one radical (assuming index is same).Step 3: Simplify radical.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Example A.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Example B.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Example C.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

Challenge:

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

What have we learned about the products of rational and irrational numbers?

Go back to your rational and irrational chart.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

How would you describe the following? Give 2 examples of each.

The product of a rational and a rational.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

How would you describe the following? Give 2 examples of each.

The product of an irrational and an irrational.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019

How would you describe the following? Give 2 examples of each.

The product of a rational and an irrational.

4 ­ Notes ­ Simplifying and Multiplying Radicals.notebook January 09, 2019