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.