Why Square Root Of 2 Is Irrational
A step-by-step animated proof by contradiction showing that √2 cannot be written as a fraction. Starting from the assumption √2 = a/b with no common factors, the animation walks through squaring both sides, showing a² = 2b², proving a must be even, substituting a = 2k, and showing b must also be even — contradicting the original assumption. Colorful visuals, a number line, and clean equation animations make the logic clear for grade 9 students learning proof techniques.
Narrated · 9:16 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Create a 45–60 second vertical 9:16 educational mathematics animation explaining why √2 is an irrational number. Target audience: Class 8–10 students. Start with the hook: “Can you write √2 as a fraction?” Show √2 ≈ 1.41421356... and explain that the decimal continues without repeating. Then give a simple proof by contradiction: Assume √2 = a/b, where a and b are integers with no common factor. Square both sides: 2 = a²/b² Therefore: a² = 2b² Explain visually that a² must be even, so a must be even. Let a = 2k. Substitute: 4k² = 2b² Therefore: b² = 2k² So b must also be even. This contradicts the assumption that a and b have no common factor. Conclude: “Therefore √2 cannot be written as a fraction. √2 is irrational.” Use clean animated equations, a number line, smooth zooms, and minimal text. Do not skip logical steps. Keep all mathematical notation accurate. Audience: grade 9th students Teaching plan: make it engaging and make It colourfull and vibrant
Make the next one in this series
- Prove that √3 and √5 are also irrational using the same method
- Show a visual proof of the Pythagorean theorem using animated squares
- Explain rational vs irrational numbers with a colorful number line animation
