Lesson 65: Adding & Subtracting Radicals

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson focuses on adding and subtracting radicals. Students will learn to combine like radicals, simplify radical expressions, and understand the rules for operations involving radicals.

Learning Objectives

• Identify like radicals and unlike radicals.
• Learn to add and subtract radicals with the same radicand.
• Simplify radical expressions after addition or subtraction.

Topics Covered

• Like radicals
• Adding radicals
• Subtracting radicals

Key Terms

• Like Radicals: Radicals with the same radicand and index.
• Unlike Radicals: Radicals with different radicands or indexes that cannot be directly combined.
• Simplify: To rewrite a radical expression in its simplest form.

Lesson Examples

Example 1: Adding Like Radicals

1. Add √12 + 3√12.
2. Combine coefficients: 1 + 3 = 4.
3. Answer: 4√12.

Example 2: Subtracting Like Radicals

1. Subtract 5√18 − 2√18.
2. Combine coefficients: 5 − 2 = 3.
3. Answer: 3√18.

Practice Problems

1. 2√5 + 3√5
2. 7√3 − 4√3
3. 5√2 + 2√8
4. 3√12 − √12

Tips & Common Mistakes

• Only combine like radicals; different radicands cannot be added directly.
• Always simplify radicals before adding or subtracting.
• Remember to combine coefficients, not radicands.

Summary

Radicals can be added or subtracted only when they are like radicals. Simplifying expressions first and combining coefficients ensures correct results. Unlike radicals must remain separate unless simplified to like radicals.

Challenge Problems

1. √50 + 2√8
2. 3√18 − √8
3. 5√32 + 2√8