Cube Root 1 to 20
In mathematics, the cube root of a number is the value that, when multiplied by itself three times, gives the original number. Cube roots are essential in algebra, geometry, and real-world applications like engineering, physics, and architecture.
For example, the cube root of 8 is 2, because:
2 × 2 × 2 = 8
In this article, we will cover:
- Cube Roots Definition
- Cube Root Table 1 to 20
- Cube of 1 to 20
- Methods to Find Cube Roots
- Real-Life Applications
- Solved Examples
- FAQs
What is a Cube Root?
The cube root of a number x is written as 3√x and represents a value that, when cubed, results in x.
Mathematical Representation
3√x = y if y3 = x
Loading PDF...
For example:
- 3√27 = 3 because 33 = 27
- 3√125 = 5 because 53 = 125
Unlike square roots, cube roots can be both positive and negative:
- 3√-27 = -3 since (-3) × (-3) × (-3) = -27
Cube Root Table 1 to 20
| Number | Cube Root (Approx.) |
| 1 | 1.000 |
| 2 | 1.260 |
| 3 | 1.442 |
| 4 | 1.587 |
| 5 | 1.710 |
| 6 | 1.817 |
| 7 | 1.913 |
| 8 | 2.000 |
| 9 | 2.080 |
| 10 | 2.154 |
| 11 | 2.224 |
| 12 | 2.289 |
| 13 | 2.351 |
| 14 | 2.410 |
| 15 | 2.466 |
| 16 | 2.520 |
| 17 | 2.571 |
| 18 | 2.621 |
| 19 | 2.668 |
| 20 | 2.714 |
Cubes of 1 to 20
| Number | Cube(n3) |
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1000 |
| 11 | 1331 |
| 12 | 1728 |
| 13 | 2197 |
| 14 | 2744 |
| 15 | 3375 |
| 16 | 4096 |
| 17 | 4913 |
| 18 | 5832 |
| 19 | 6859 |
| 20 | 8000 |
Methods to Find Cube Roots
1. Prime Factorization Method
Useful for perfect cubes. Example: Find 3√216.
- Prime factors: 216 = 2 × 2 × 2 × 3 × 3 × 3
- Group into triples: (2×2×2) × (3×3×3)
- Take one number from each group: 2 × 3 = 6
2. Estimation Method
Useful for non-perfect cubes. Example: Find 3√50.
- Perfect cubes near 50: 27 and 64
- Approximate cube root: ~3.7
3. Long Division Method
Useful for precise cube roots but a lengthy process.
How to Calculate the Values of Cube 1 to 20?
To calculate the cube of numbers from 1 to 20, you simply multiply the number by itself twice. In mathematical terms, cube of a number n is n × n × n.
For example:
- Cube of 2 = 2 × 2 × 2 = 8
- Cube of 5 = 5 × 5 × 5 = 125
- Cube of 10 = 10 × 10 × 10 = 1000
You can continue this method for all numbers up to 20.
If you want faster results, you can also memorize common cubes or use a scientific calculator to compute them quickly.
| Also Check |
| Associative Property |
| Centroid of a Triangle |
| Collinear Points |
| Commutative Property |
| Cos 0 |
| Hypotenuse |
Real-Life Applications of Cube Roots
- Engineering and Construction: Calculate dimensions of objects.
- Physics and Chemistry: Use in fluid dynamics and molecular structures.
- Computer Science & Data Science: Algorithms involve cube roots for data normalization.
- Finance and Economics: Compound interest calculations use cube roots.
Solved Examples cube root of 1 to 20
Q. Evaluate 4 times 10 cube plus 9
Solution: 4 × 103 + 9 = 4 × 1000 + 9 = 4009
Q. Find the value of ∛20-2+(53).
Solution: ∛20 = 2.714
53 = 125
Therefore,
∛20-2+(53) = 2.714 – 2 + 125
= 125.714
Q. Solve 10-∛6.
Solution: ∛6 = 1.817
Therefore,
10-∛6 = 10 – 1.817 = 8.183
Q. Solve ∛3+33.
Solution: ∛3+33
The value of:
∛3 = 1.442
33 = 27
Therefore,
∛3+33 = 1.442 + 27 = 28.442
1 to 20 cube root FAQs
What is the cube root of 1 to 20?
The cube roots of numbers from 1 to 20 are approximate values that tell you what number multiplies by itself three times to give the original number. For example, ∛1 = 1 and ∛8 = 2. The cube roots between 1 and 20 range from 1 to about 2.714.
What is the √ 1 to 20?
The square roots of numbers from 1 to 20 are values that, when squared, give the original number. For example, √4 = 2 and √9 = 3. The square roots start at 1 for 1 and go up to approximately 4.472 for 20.
What are the cubes 1 to 30?
The cubes of numbers from 1 to 30 are the results of multiplying a number by itself twice. For example, 2³ = 8, 3³ = 27, and so on. Some important cubes are:
- 1³ = 1
- 5³ = 125
- 10³ = 1000
- 20³ = 8000
- 30³ = 27000
How to solve cube 1 to 20?
To find the cube of numbers from 1 to 20, simply multiply the number by itself twice. For example:
- Cube of 3 = 3 × 3 × 3 = 27
- Cube of 7 = 7 × 7 × 7 = 343
What are the perfect cubes from 1 to 20?
Perfect cubes between 1 and 20 are numbers that are cubes of whole numbers. Only two numbers qualify:
- 1³ = 1
- 2³ = 8
There are no other perfect cubes under 20.
Is 20 a perfect cube root?
No, 20 is not a perfect cube. A perfect cube has an exact whole number as its cube root, but ∛20 is approximately 2.714, which is not an integer.
How to find the cube root of 197?
To find the cube root of 197, you can:
- Use a calculator to get ∛197 ≈ 5.817
- Estimate between nearby perfect cubes (125 and 216) since 197 lies between 5³ and 6³.
- Apply successive approximation if needed for a closer manual estimate.