Finding Square Roots of Large Numbers by Factoring

The Organic Chemistry Tutor

This instructional mathematics video demonstrates how to calculate the square roots of large numbers without the use of a calculator. The narrator guides viewers through three specific examples involving four- and five-digit numbers (1,444, 4,096, and 11,664), showing a step-by-step process of breaking these numbers down into their prime factors. By creating factor trees and identifying pairs of identical factors or known perfect squares, the video simplifies complex radicals into manageable multiplication problems. Key themes explored include prime factorization, properties of radicals, mental math strategies for division, and the recognition of perfect squares. The video specifically emphasizes the strategy of repeatedly dividing even numbers by 2 to reduce them to recognizable components. It also introduces a mental math technique for dividing large numbers by decomposing them into place values (e.g., breaking 11,664 into 10,000 + 1,600 + 64 to divide by 2). For educators, this video serves as an excellent resource for teaching Number Sense and Algebra concepts. It helps students build confidence in handling large numbers and reinforces the connection between exponents and roots. The method shown is particularly useful for standardized test preparation where calculators may be prohibited, encouraging students to rely on arithmetic fluency and structural understanding of numbers rather than rote computation.