New Numbers പുതിയ സംഖ്യകൾ
The diagonal of a square with sides 1 metre is longer than 1 and shorter than 2 – but no fraction gives its exact length. This chapter meets the first numbers that are not fractions, gives them names like √2 and √3, learns to pin them down with decimals, and adds and subtracts them. 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, the appendix proof made gentle, 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 let you try fractions, add decimal places and change lengths. Watching a square's area creep towards 2 but never reach it is the fastest way to feel what √2 is.
✍️ Try before you see
Questions come with a Show a hint button and a hidden final answer. 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 19–32).
Learning path
Follow the pages in order. If you are confident with square roots of perfect squares, squaring fractions, Pythagoras and odd/even numbers, you may skim pages 1–4, but do try their quizzes.
The chapter in one picture
The yellow square has side 1 m. The blue square stands on its diagonal and has area exactly 2 sq m. Slide to choose a side for the green square and watch its area: 1.4 is too small, 1.5 is too big, 1.41 is too small, 1.42 is too big… The exact side is a new number, √2 = 1.41421…, that no fraction can name. That is this chapter.
Quick glossary (Malayalam ↔ English)
| Textbook term | English | Meaning |
|---|---|---|
| എണ്ണൽസംഖ്യ | Natural (counting) number | 1, 2, 3, … |
| ഭിന്നസംഖ്യ | Fraction (rational number) | A number that can be written as one natural number over another, like ½, 1⅓, 1.41 = 1 41/100 |
| അധിസംഖ്യ | Positive number | Any number greater than 0 |
| വർഗം / വർഗമൂലം | Square / square root | x² = x × x; √x is the number whose square is x |
| വികർണ്ണം | Diagonal | The line joining opposite corners of a square |
| പരപ്പളവ് / ചുറ്റളവ് | Area / perimeter | Space inside a figure / length around it |
| മട്ടത്രികോണം | Right triangle | A triangle with a 90° angle |
| കർണ്ണം / ലംബവശങ്ങൾ | Hypotenuse / perpendicular sides | The longest side, opposite the right angle / the two sides that make the right angle |
| സമഭുജത്രികോണം | Equilateral triangle | All three sides equal |
| ദശാംശരൂപം | Decimal form | 1.41421… is the decimal form of √2 |
| ഏകദേശം (≈) | Approximately | √2 ≈ 1.41 means "close to, but not exactly" |
| ഘനം / വ്യാപ്തം | Cube / volume | A cube of volume 2 has side ∛2, also not a fraction |
| അനുബന്ധം | Appendix | The proof that no fraction squares to 2 |
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.