Simplificación de Raíces Parte 1.

Simplification of Radicals: Key Concepts and Examples

Introduction to Radical Simplification

• The video introduces the topic of radical simplification in algebra, emphasizing its importance through two example exercises.

First Example: Simplifying √72

• The first step involves decomposing 72 into its prime factors: 72 = 2 × 36, 36 = 2 × 18, 18 = 2 × 9, and finally, 9 = 3 × 3.

• After identifying pairs of equal numbers (two pairs of '2' and one pair of '3'), the products are calculated as follows: 2 times 2 = 4 and 3 times 3 = 9.

• These values are substituted back into the radical expression resulting in √(4 × 9 × 2), which can be separated using a property of radicals.

• Applying this property yields √4 × √9 × √2; where √4 equals '2', √9 equals '3', and √2 remains under the radical.

• The final simplification results in 6√2, demonstrating how to combine integer results from exact roots with remaining radicals.

Second Example: Simplifying √160

• Similar to the first example, we decompose the number inside the root: 160 = 80 (half), then down to pairs until reaching prime factors.

• Identifying pairs reveals two pairs of '2' and one unpaired value. The unpaired values are multiplied together (e.g., 2 times5).

• This leads to substituting back into the radical as √(4 × 4 ×10), separating them into individual square roots for simplification.

• The result is simplified to 4√10. This example highlights how different configurations of paired/unpaired values affect simplification outcomes.

Conclusion

• Both examples illustrate key techniques in simplifying radicals by focusing on prime factorization and recognizing pairs. Understanding these steps is crucial for mastering radical simplifications in algebra.