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By Karan Singh Bisht
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Updated on 28 Apr 2025, 12:28 IST
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:
The cube root of a number x is written as 3√x and represents a value that, when cubed, results in x.
3√x = y if y3 = x
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For example:
Unlike square roots, cube roots can be both positive and negative:
| 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 |
| 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 |
1. Prime Factorization Method
Useful for perfect cubes. Example: Find 3√216.
2. Estimation Method
Useful for non-perfect cubes. Example: Find 3√50.
3. Long Division Method
Useful for precise cube roots but a lengthy process.
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:
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 |
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
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.
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.
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:
To find the cube of numbers from 1 to 20, simply multiply the number by itself twice. For example:
Perfect cubes between 1 and 20 are numbers that are cubes of whole numbers. Only two numbers qualify:
There are no other perfect cubes under 20.
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.
To find the cube root of 197, you can: