Roots Between the Squares

Mental Math · Axiom Academy

Master the art of approximating square roots mentally using perfect squares and clever reasoning! Building Blocks: Perfect Squares Before we estimate square roots, we need to know our perfect squares . These are the foundation of mental estimation! Click on each box to see the relationship. To estimate √20, we "sandwich" 20 between two perfect squares. This tells us the answer must be between their roots! Since 20 is closer to 16 than to 25, √20 should be closer to 4 than to 5! Let's get more precise! We can use the distance from perfect squares to make better estimates. Now it's your turn! Estimate these square roots to one decimal place. Sandwich: Find the perfect squares on either side Narrow: Determine which root it's closer to Estimate: Make your approximation to one decimal Square root estimation helps with: calculating distances, understanding areas and dimensions, verifying calculator results, physics problems (like finding velocity from kinetic energy), and quickly gauging magnitudes in everyday situations!

This is the written version of the interactive lesson above. See the full Mental Math course.