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Common Core For Geometry

Worksheets for Geometry, Module 2, Lesson 23

Student Outcomes

- Students use the distributive property to simplify expressions that contain radicals.

**Adding and Subtracting Expressions with Radicals**

Classwork

**Exercises 1–5**

Simplify as much as possible.

- √32 =
- √45 =
- √300 =
- The triangle shown below has a perimeter of 6.5√2 units. Make a conjecture about how this answer was reached.
- The sides of a triangle are 4√3, √12, and √75. Make a conjecture about how to determine the perimeter of this triangle.

**Exercises 6**

- Circle the expressions that can be simplified using the distributive property. Be prepared to explain your choices.

**Example 1**

Explain how the expression 8.3√2+ 7.9√2 can be simplified using the distributive property. Explain how the expression 11√7− 6√7+ 3√2 can be simplified using the distributive property.

**Example 2**

Explain how the expression 19√2+ 2√8 can be simplified using the distributive property.

**Example 3**

Can the expression √7+ 2√10 be simplified using the distributive property? To determine if an expression can be simplified, you must first simplify each of the terms within the expression. Then, apply the distributive property, or other properties as needed, to simplify the expression.

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