Simplificación de Raíces Parte 3.

Simplification of Radicals: Example Analysis

Prime Factorization Process

• The example begins with the number 4,356 under a square root. The goal is to simplify this radical by finding its prime factors.

• The first step involves dividing 4,356 by 2, yielding 2,178. This process continues as the speaker checks for divisibility by smaller prime numbers.

• Further division reveals that 2,178 can be divided again by 2 to get 1,089. The speaker then tests for divisibility by 3 and finds that it is indeed divisible.

Continuing Factorization

• After determining that 1,089 can be divided by 3 to yield 363, the speaker sums the digits (3 + 6 + 3 = 12), confirming it's a multiple of three.

• Continuing with factorization leads to identifying that both factors of the resulting numbers are paired correctly: pairs of two (4), three (9), and eleven (121).

Final Steps in Simplification

• All values have been paired successfully without any remaining unpaired factors. The simplification results in separating into three distinct roots: √4, √9, and √121.

• Each root simplifies down to integers: √4 = 2, √9 = 3, and √121 =11. Thus leading towards a complete simplification of the original radical expression.

This structured approach highlights key steps in simplifying radicals through prime factorization while ensuring clarity on how each number contributes to the final result.