B. In the second column rewrite your circled expressions by combining like terms (using the distributive property). Lesson 18: Adding and Subtracting ...
Lesson 18: Adding and Subtracting Expressions with Radicals Opening Exercise (Note: triangles are not to scale.) 1. The triangle shown below has a perimeter of 6.5√2 units. Make a conjecture about how this answer was reached.
2. The triangle shown below has a perimeter of 2 2 + 5 3 . Make a conjecture about how this answer was reached.
3. The sides of a triangle are 4√3, √12, and √75. Make a conjecture about how to determine the perimeter of this triangle.
Lesson 18: Unit 5:
Adding and Subtracting Expressions with Radicals Similarity and Proof
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Lesson 18
Hart Interactive – Geometry
M2
GEOMETRY
Adding radicals is analogous to adding expressions with variables. The radical portion of the expression must be the same for the coefficients to be added together.
4. A. Circle the expressions that can be simplified by combining like terms. Be prepared to explain your choices. 8.3√2 + 7.9√2 √13 − √6
−15√5 + √45
11√7 − 6√7 + 3√2 19√2 + 2√8 4 + √11
√7 + 2√10 √12 − √75 √32 + √2
6√13 + √26
B. In the second column rewrite your circled expressions by combining like terms (using the distributive property).
Lesson 18: Unit 5:
Adding and Subtracting Expressions with Radicals Similarity and Proof
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Lesson 18
Hart Interactive – Geometry
M2
GEOMETRY
5. Explain how the expression 8.3√2 + 7.9√2 can be simplified using the distributive property. 6. Explain how the expression 11√7 − 6√7 + 3√2 can be simplified using the distributive property. 7. Explain how the expression 19√2 + 2√8 can be simplified using the distributive property. 8. Can the expression √7 + 2√10 be simplified using the distributive property? Explain your thinking.
9. Multiplying two radical expressions that also include addition or subtraction can be organized using a table or with double distribution. The product
(
3+ 5
)
)(
6 − 15 has been started with both methods
below. Choose one of the method and have your partner do the other method. Be sure you both get the same answer. Table Method
(
3+ 5
3
)(
6 − 15
Double Distribution
)
(
3+ 5 3
5
(
)(
6 − 15
)
6 − 15 + 5
(
) )
6 − 15 =
6
− 15 Simplify and combine like terms.
(
3+ 5
)(
)
6 − 15 = _______________________
Lesson 18: Unit 5:
(
3+ 5
)(
Adding and Subtracting Expressions with Radicals Similarity and Proof
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Lesson 18
Hart Interactive – Geometry
M2
GEOMETRY
10. A. Fill in the chart below by multiplying the column and row as you would in a multiplication table. X
2
5
6+ 2
3− 5
3
9
6− 2
5
B. Circle all the products that are rational numbers.
Lesson Summary 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.
Don’t assume that expression with unlike radicals cannot be simplified. It is possible that, after simplifying the radical, the expression can be simplified.
Lesson 18: Unit 5:
Adding and Subtracting Expressions with Radicals Similarity and Proof
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Lesson 18
Hart Interactive – Geometry
M2
GEOMETRY
10. CIVIL ENGINEERING: An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round your answer to the nearest hundredth.
11. What is the perimeter of the triangle shown below?
12. Determine the area and perimeter of the triangle shown. Simplify as much as possible.
Lesson 18: Unit 5:
Adding and Subtracting Expressions with Radicals Similarity and Proof
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Lesson 18
Hart Interactive – Geometry
M2
GEOMETRY
13. Determine the area and perimeter of the rectangle shown. Simplify as much as possible.
14. Determine the area and perimeter of the triangle shown. Simplify as much as possible.
15. Determine the area and perimeter of the triangle shown. Simplify as much as possible.
16. The area of the rectangle shown in the diagram below is 160 square units. Determine the area and perimeter of the shaded triangle. Write your answers in simplest radical form, and then approximate to the nearest tenth.
Lesson 18: Unit 5:
Adding and Subtracting Expressions with Radicals Similarity and Proof
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Lesson 18
Hart Interactive – Geometry
M2
GEOMETRY
17. CHALLENGE Parallelogram 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 has an area of 9√3 square units. 𝐷𝐷𝐷𝐷 = 3√3, and 𝐺𝐺 and 𝐻𝐻 are ���� , respectively. Find the area of the shaded region. Write your answer in simplest ���� and 𝐶𝐶𝐶𝐶 midpoints of 𝐷𝐷𝐷𝐷 radical form.
Lesson 18: Unit 5:
Adding and Subtracting Expressions with Radicals Similarity and Proof