Cube Roots from 1 to 20 Table (With Solutions)
The concept of cube root 1 to 20 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Knowing the cube roots of numbers from 1 to 20 makes it much easier for students to solve questions quickly, especially in mental maths or during time-based competitive exams.
What Is Cube Root 1 to 20?
A cube root 1 to 20 is the value which, when multiplied by itself three times (cubed), gives a number between 1 and 20. In simple words, the cube root of a number n is a value x such that \( x \times x \times x = n \). You’ll find this concept applied in areas such as volume calculation, algebraic factorization, and many number system problems in Olympiads and JEE.
Key Formula for Cube Root 1 to 20
Here’s the standard formula: \( \sqrt[3]{n} = x \), where \( x \) is the cube root of \( n \). For all numbers from 1 to 20, you can use this cube root formula to find quick values for exam-based questions.
Cube Roots from 1 to 20 Table
Cube roots from 1 to 20 are values which, when raised to the power of 3, result in numbers from 1 to 20. Here is a table of cube roots for numbers 1 to 20, useful for maths exams and quick mental calculations.
| Number (n) | Cube (n³) | Cube Root (∛n) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 8 | 1.260 |
| 3 | 27 | 1.442 |
| 4 | 64 | 1.587 |
| 5 | 125 | 1.710 |
| 6 | 216 | 1.817 |
| 7 | 343 | 1.913 |
| 8 | 512 | 2 |
| 9 | 729 | 2.080 |
| 10 | 1000 | 2.154 |
| 11 | 1331 | 2.224 |
| 12 | 1728 | 2.289 |
| 13 | 2197 | 2.351 |
| 14 | 2744 | 2.410 |
| 15 | 3375 | 2.466 |
| 16 | 4096 | 2.520 |
| 17 | 4913 | 2.571 |
| 18 | 5832 | 2.621 |
| 19 | 6859 | 2.668 |
| 20 | 8000 | 2.714 |
How to Calculate Cube Root 1 to 20
You can find the cube root 1 to 20 by estimation, using the prime factorization method for perfect cubes, or using a calculator for quick decimals.
- For perfect cubes (like 8, 27, 64), just find what number times itself three times gives the value.
- For others (like 5, 9, 20), estimate between known cubes or use calculator/exam tables.
- Tip: For mental maths, remember that ∛8 = 2, ∛27 = 3, ∛64 = 4, and then fill in values in between.
Step-by-Step Cube Root Example
Find the cube root of 8.
1. 8 can be written as \( 2 \times 2 \times 2 \)2. Therefore, \( \sqrt[3]{8} = 2 \)
Find the cube root of 19 (approximate).
1. Perfect cubes near 19 are 8 (2³) and 27 (3³).2. Take the cube root of 19 as between 2 and 3.
3. Using calculator/table: ∛19 ≈ 2.668
Questions like these are seen in competitive exams and school tests.
Speed Trick or Vedic Shortcut
Here’s a quick method for cube root 1 to 20 especially for perfect cubes: If the last digit of the number is 8, its cube root will be 2 (since 2 × 2 × 2 = 8). Similarly, if it's 7, think 3. For decimals, estimate between cubes you do know. Tricks like these are strong aids in exam conditions. Vedantu’s live sessions offer more such shortcuts for speed and accuracy.
Cross-Disciplinary Usage
Cube root 1 to 20 is not only useful in Maths but also plays an important role in Physics (density and volume), Computer Science (data structuring), and logical reasoning. Students preparing for JEE or NEET will see its relevance in various exam questions, especially where simplification is critical.
Try These Yourself
- What is the cube root of 125?
- Which number between 1 and 20 has a cube root equal to 3?
- Estimate the cube root of 10 up to two decimal places.
- List all perfect cubes from 1 to 20 and their cube roots.
Frequent Errors and Misunderstandings
- Confusing square roots with cube roots (∛ vs √).
- Using wrong cube numbers in tables during exams.
- Assuming all cube roots between 1 and 20 are whole numbers (most are decimals).
Relation to Other Concepts
The idea of cube root 1 to 20 connects closely with topics such as Cube 1 to 20 and Square Root 1 to 20. Mastering this helps students handle complex algebraic factorization, exponents, and polynomial equations efficiently in higher classes.
Classroom Tip
A quick way to remember cube root 1 to 20 is to memorize perfect cubes and their roots using a hand-written table posted on your study wall. You can also use patterns—for example, cubes end with the same digits as their root (2³=8 ends with 8, 3³=27 ends with 7)—to help with quick recall. Vedantu’s teachers often recommend making your own chart for effective revision.
Wrapping It All Up
We explored cube root 1 to 20—from definition, formula, examples, mistakes, and its connection to other subjects. Continue practicing with Vedantu and use this table often to do faster, error-free calculations during your maths journey.
Related Vedantu Pages
- Cube Root Table – For a printable table and reference chart.
- How to Find Cube Root – For in-depth methods and more speed tricks.
