Lesson 67: Dividing 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 teaches how to divide radicals, including simplifying radical fractions and rationalizing denominators for proper simplification.

Learning Objectives

• Understand how to divide radicals with the same or different radicands.
• Learn to simplify radical fractions.
• Rationalize denominators when necessary.

Topics Covered

• Dividing like radicals
• Dividing unlike radicals
• Rationalizing denominators

Key Terms

• Radical Fraction: A fraction where the numerator or denominator (or both) contains a radical.
• Rationalize Denominator: Rewriting a fraction so that the denominator has no radicals.
• Like Radicals: Radicals with the same radicand and index that can be directly divided.

Lesson Examples

Example 1: Dividing Like Radicals

1. Divide √50 ÷ √2.
2. Combine under a single radical: √(50 ÷ 2) = √25.
3. Simplify: √25 = 5.

Example 2: Dividing Unlike Radicals & Rationalizing Denominator

1. Divide 3 ÷ √3.
2. Multiply numerator and denominator by √3: (3√3)/(√3√3) = (3√3)/3.
3. Simplify: (3√3)/3 = √3.

Practice Problems

1. √72 ÷ √2
2. √45 ÷ √5
3. 5 ÷ √20
4. 2√6 ÷ √3

Tips & Common Mistakes

• Always simplify radicals before dividing when possible.
• Remember to rationalize denominators to avoid leaving radicals in the denominator.
• Do not confuse dividing radicals with multiplying radicals; the rules differ slightly.

Summary

Dividing radicals requires simplifying expressions and, when necessary, rationalizing denominators. Like radicals can be combined under a single radical, while unlike radicals may need multiplication to remove radicals from the denominator.

Challenge Problems

1. √128 ÷ √2
2. 7 ÷ √7
3. 3√18 ÷ √2