Irrational Numbers അഭിന്നകഗുണനം
Multiplying and dividing numbers like √2 and √3, writing them in simplest form, and using them to find the areas of triangles – all the way to Heron's famous formula. An interactive, animated self-study guide: the basics from earlier classes, every idea of the chapter with real-life examples, animated solutions to every textbook question, a revision sheet, and a model test with a fully solved paper.
How to use this guide
🎬 Watch the animations
Every idea has a step-by-step animation. Press Next ▶ to move one step at a time, or ▶▶ Auto play to watch it like a video. You can go back any time.
🖐️ Play with the numbers
Sliders change side lengths, decimal places and scale. Watching the numbers and pictures change together is the fastest way to feel why a rule is true.
✍️ Try before you see
Questions come with a Show answer button. Always attempt the question in your notebook first, then check. The quizzes give instant feedback.
📖 Textbook links
Purple മലയാളം words are the exact terms used in your textbook, so you can match every page here with the book (pages 83–98).
Learning path
Follow the pages in order. If you remember square roots and Pythagoras well, you may skim pages 1–4, but do try their quizzes.
The chapter in one picture
Start with a right triangle with legs 1 and 1: the hypotenuse is √2. Add a new leg of length 1 at right angles to that hypotenuse and you get √3, then √4 = 2, √5, … Every one of these is an exact length you can draw, even though most of them can never be written as a fraction. This chapter teaches you to multiply and divide such numbers and to use them for areas.
Quick glossary (Malayalam ↔ English)
| Textbook term | English | Meaning |
|---|---|---|
| അഭിന്നകസംഖ്യ | Irrational number | A number that cannot be written as a fraction p/q, e.g. √2, √3, π |
| ഭിന്നസംഖ്യ | Fraction / rational number | Can be written as p/q: ½, 0.75, 3 |
| വർഗമൂലം | Square root | √x is the positive number whose square is x |
| വർഗം | Square (of a number) | x² = x × x |
| ഗുണനം / ഹരണം | Multiplication / division | √x × √y = √(xy); √x ÷ √y = √(x/y) |
| ദശാംശം | Decimal | 1.414… is the decimal form of √2 |
| പരപ്പളവ് / ചുറ്റളവ് | Area / perimeter | Space inside / length around |
| സമഭുജത്രികോണം | Equilateral triangle | All three sides equal; height = (√3/2) × side |
| സമപാർശ്വത്രികോണം | Isosceles triangle | Two sides equal |
| ലംബകം | Trapezium | Quadrilateral with one pair of parallel sides |
| സമഷഡ്ഭുജം | Regular hexagon | Six equal sides = six equilateral triangles |
| ഹെറോൺ സൂത്രവാക്യം | Heron's formula | Area = √(s(s−a)(s−b)(s−c)), s = half the perimeter |
Made for self-learning. Works offline – every page is a single file. Study material prepared by Claude for Madhu's family study folder, October 2026.