Adding and Subtracting Expressions with Radicals

New York State Common Core Math Geometry, Module 2, Lesson 23

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.

1. √32 =
2. √45 =
3. √300 =
4. The triangle shown below has a perimeter of 6.5√2 units. Make a conjecture about how this answer was reached.
5. The sides of a triangle are 4√3, √12, and √75. Make a conjecture about how to determine the perimeter of this triangle.

• Show Video

Exercises 6

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.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.