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).
What is the Value of cos(15°)?
Learn the exact mathematical value of cos 15 degrees. See the step-by-step derivation using the cosine subtraction formula cos(A-B) = cos(45-30).
What is the Value of Cos 15°? (Derivation & Formula)
Learn the exact value of cos 15 degrees in fraction and decimal form. See the step-by-step derivation using the cos(A-B) formula.
What is the Value of Cos 37° in Fraction?
Learn the exact fractional value of cos 37 degrees (4/5) used in physics and math. Understand how it is derived from the famous 3-4-5 right-angled triangle.
What is the Value of cot(30°)?
Learn the exact value of cot 30 degrees. Understand how to easily derive it using the inverse of tan(30) or the ratio of cos(30) divided by sin(30).
What is the value of log₄(2)?
Learn how to mathematically solve log base 4 of 2 (log₄ 2). Understand the fundamental massive properties of logarithms with step-by-step calculation.
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