Simplificación de Raíces Parte 2.
Simplification of Radicals: Example with √750
Introduction to Radical Simplification
- The instructor introduces the topic of simplifying radicals, specifically focusing on the square root of 750.
- Emphasis is placed on decomposing the number under the radical into its prime factors.
Prime Factorization Process
- The first step involves dividing 750 by 2, resulting in 375. This demonstrates how to begin factorization.
- Continuing with factorization, 375 is divided by 5 to yield 75, showcasing another method for breaking down numbers.
Identifying Pairs and Remaining Values
- The instructor identifies pairs among the factors; specifically noting a pair of fives that multiply to form 25.
- It is highlighted that not all values have pairs; thus, remaining unpaired values (2, 3, and an additional 5) must be grouped together for further simplification.
Final Steps in Simplification
- The product of the unpaired values (5 * 2 * 3 = 30) is calculated and prepared for substitution back into the radical.
- The final expression separates into two roots: √25 and √30. This leads to a simplified result of 5sqrt30, demonstrating effective radical simplification techniques.