Understanding how to square (n × n) and cube (n × n × n) numbers is essential for solving area and volume problems in geometry. While you should memorize squares up to 30, it is good to know cubes up to at least 15.
The number 64 is mathematically special because it is both a perfect square (8² = 64) AND a perfect cube (4³ = 64).
Here are the most frequently used numbers in exams:
| Number (n) | Square (n²) | Cube (n³) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1000 |
| 11 | 121 | 1331 |
| 12 | 144 | 1728 |
| 13 | 169 | 2197 |
| 14 | 196 | 2744 |
| 15 | 225 | 3375 |
The cube of a negative number is ALWAYS negative. For example, (-2)³ = -2 × -2 × -2 = -8. (However, the square of a negative number is always positive).
Value of tan 30°
tan 30° = 1/√3 = √3/3 ≈ 0.5774. Derived from a 30-60-90 triangle: opposite side = 1, adjacent side = √3. Learn with trig table and FAQs.
वर्ग किसे कहते हैं? (Square in Mathematics)
जानें गणित में वर्ग (Square) किसे कहते हैं। वर्ग की परिभाषा, क्षेत्रफल (Area), परिमाप (Perimeter) के सूत्र और इसके प्रमुख गुण (Properties) हिंदी में समझें।
Vectors — Displacement Problems (Class 10 & 11)
Solve vectors and displacement problems. If a car moves 17 km north from point A, learn resultant displacement using Pythagoras and vector addition for Class 10.
What are the Vertices of a Triangle?
Learn what the vertices of a triangle are in Geometry. Understand the corners, how they connect edges, and how they are used to name shapes.
Math Word Problem: Discount and Profit/Loss
Learn how to solve typical math word problems involving discounts, selling price, and profit/loss percentage using basic algebra and formulas.
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