How to Calculate Cube Root Step by Step with Formula & Examples
Cube Root Calculator
What is Cube Root Calculator?
A Cube Root Calculator is a free online tool that helps you find the cube root (∛n) of any number instantly and accurately. It simplifies the process of finding cube roots for both perfect cubes and non-perfect cubes, including positive and negative numbers. Enter your value, click calculate, and instantly get the result with steps. Whether you’re a student, a teacher, or simply looking to solve maths problems, this calculator is designed to make cube root calculations quick and easy.
Formula or Logic Behind Cube Root Calculator
The cube root of a number \( n \) is a number \( x \) such that \( x^3 = n \). In mathematical terms, the cube root is written as ∛n or \( n^{1/3} \). For instance, the cube root of 125 is 5 because \( 5 × 5 × 5 = 125 \).
Cube Root Formula:
∛n = n1/3
Methods to Find Cube Root:
- Prime Factorization: Break the number into prime factors, group them in threes, and take out one from each group. E.g., ∛216 = ∛(2×2×2×3×3×3) = 2×3 = 6.
- Estimation/Calculator: For non-perfect cubes, use a calculator or estimation to get a decimal answer. E.g., ∛10 ≈ 2.154.
- Negative Numbers: The cube root of a negative number is negative. For example, ∛(-64) = -4.
Cube Roots of Numbers Table (1 to 30 & Perfect Cubes)
| Number (n) | Cube Root (∛n) |
|---|---|
| 1 | 1 |
| 2 | 1.26 |
| 3 | 1.4422 |
| 4 | 1.5874 |
| 5 | 1.7100 |
| 6 | 1.8171 |
| 7 | 1.9129 |
| 8 | 2 |
| 9 | 2.0800 |
| 10 | 2.1544 |
| 11 | 2.2239 |
| 12 | 2.2894 |
| 13 | 2.3513 |
| 14 | 2.4101 |
| 15 | 2.4662 |
| 16 | 2.5198 |
| 17 | 2.5713 |
| 18 | 2.6207 |
| 19 | 2.6684 |
| 20 | 2.7144 |
| 21 | 2.7589 |
| 22 | 2.8020 |
| 23 | 2.8439 |
| 24 | 2.8845 |
| 25 | 2.9240 |
| 26 | 2.9625 |
| 27 | 3 |
| 28 | 3.0366 |
| 29 | 3.0723 |
| 30 | 3.1072 |
| 64 | 4 |
| 125 | 5 |
| 216 | 6 |
| 343 | 7 |
| 512 | 8 |
| 729 | 9 |
| 1000 | 10 |
| 1728 | 12 |
| 2197 | 13 |
| 2744 | 14 |
Steps to Use the Cube Root Calculator
- Enter the required number or values (positive or negative).
- Click on the 'Calculate' button.
- Get instant results with the cube root value and solution steps.
Why Use Vedantu’s Cube Root Calculator?
Vedantu’s Cube Root Calculator is designed for accuracy, speed, and ease-of-use. It’s mobile-friendly, provides instant and clear solutions, and supports both positive and negative numbers. Powered by certified maths educators and trusted by millions of Indian students, it helps you build confidence with every calculation—ideal for classwork, exams, homework, and competitive preparation. Try it as a quick reference or for learning cube root concepts step by step.
Real-life Applications of Cube Root Calculator
The cube root is widely used in mathematical, scientific, and real-world applications:
- Calculating the edge of a cube when the volume is known (geometry or building projects).
- Chemistry and physics: determining side length for cubic packing, crystal lattices, and density problems.
- Normalizing data in statistics or machine learning models.
- Everyday use: packing (box size from volume), construction (block dimensions), and design/3D modeling.
- Quickly solving exam questions or Olympiad problems involving perfect cubes, e.g., ∛2744 or ∛1728.
FAQs on Cube Root Calculator for Maths Students
1. What is an online Cube Root Calculator and how does it help students?
An online Cube Root Calculator is a digital tool designed to instantly find the number which, when multiplied by itself three times, equals your input number. For students, it's a very fast way to verify answers you have calculated manually using methods like prime factorisation and to easily handle large or complex numbers.
2. How do you find the cube root of a number using the prime factorisation method?
As per the CBSE syllabus, the prime factorisation method is a core technique for finding cube roots. Follow these steps:
- First, break down the given number into its prime factors.
- Next, group the identical prime factors into sets of three.
- For each complete group of three, take one factor out.
- Finally, multiply these extracted factors together to get the cube root. For example, for the number 216, the factors are (2 × 2 × 2) × (3 × 3 × 3). Taking one from each group gives 2 × 3 = 6.
3. What is a perfect cube?
A perfect cube is a natural number that is the result of multiplying an integer by itself three times. For example, 27 is a perfect cube because 3 × 3 × 3 = 27, and 64 is a perfect cube because 4 × 4 × 4 = 64. An online calculator can help you quickly check if a large number is a perfect cube.
4. Can you find the cube root of a negative number?
Yes, the cube root of a negative number is always a negative number. This is because a negative number multiplied by itself three times results in a negative product. For example, the cube root of -125 is -5, since (–5) × (–5) × (–5) = –125. This is a key difference from square roots, which cannot be found for negative numbers within the real number system.
5. What is the key difference between finding a square root and a cube root?
The main difference is the number of times the root is multiplied. For a square root, you seek a number that is multiplied by itself (two times) to get the original number (e.g., √9 = 3 because 3x3=9). For a cube root, you must find a number that is multiplied by itself three times (e.g., ³√8 = 2 because 2x2x2=8).
6. Why is the prime factorisation method a reliable way to find the cube root of perfect cubes?
This method is reliable because it deconstructs a number into its fundamental building blocks, which are its prime factors. By definition, a perfect cube is a number formed by cubing an integer. This means its prime factors must naturally appear in groups of three. By identifying and isolating these groups of three, you are perfectly reversing the cubing process to find the original root number.
7. How can understanding cube roots be applied in real-world scenarios?
The most common real-world application of cube roots is in geometry, particularly for calculating dimensions from volume. If you know the volume of a cube-shaped object, such as a shipping box or a water tank, you can find the length of one of its sides by calculating the cube root of its volume. This is essential in fields like engineering, physics, and architecture.
8. How can you estimate the cube root of a number that is not a perfect cube?
Yes, you can estimate it by finding the two perfect cubes your number lies between. For instance, to estimate the cube root of 40, you know it is between the perfect cubes 27 (³√27 = 3) and 64 (³√64 = 4). Since 40 is closer to 27 than to 64, you can deduce its cube root will be a value slightly greater than 3. An online calculator can then provide the precise decimal value, which is approximately 3.42.
