Algebra 101 - Unit 9

Lesson 53: Simplifying Radical Expressions

Simplifying radicals means rewriting them in simplest form. This involves factoring the radicand and removing perfect powers when possible. The goal is to make the radical expression as simple as possible.

Steps to Simplify Radical Expressions

1. Factor the radicand into prime factors.
2. Separate perfect squares (or cubes for cube roots) from the rest.
3. Take the root of the perfect powers and move them outside the radical.
4. Multiply or divide any remaining factors inside the radical if necessary.

Examples

Example 1: √50

• Factor: 50 = 25 × 2
• Separate: √50 = √25 × √2
• Simplify: √25 = 5 → √50 = 5√2

Example 2: √72

• Factor: 72 = 36 × 2
• Separate: √72 = √36 × √2
• Simplify: √36 = 6 → √72 = 6√2

Example 3: ∛54

• Factor: 54 = 27 × 2
• Separate: ∛54 = ∛27 × ∛2
• Simplify: ∛27 = 3 → ∛54 = 3∛2

Practice Problems

1. Simplify: √45
2. Simplify: √200
3. Simplify: ∛16
4. Simplify: √98
5. Simplify: ∛250