Quick Table: Cube Roots of Numbers 1 to 30 Explained
What is Cube Root?
The cube root of a number a is that number which when multiplied by itself three times gives the number ‘a’ itself. The cube root is the inverse operation of cubing a number. The cube root symbols is∛, it is the "radical" symbol (used for square roots) with a little three to mean cube root.
If n is a perfect cube for any integer m i.e., n = m³, then m is called the cube root of n and it is denoted by m = ∛n.
Cube root list 1 to 30 will help students to solve the cube root problem easily, accurately, and with speed.
How to Find Cube Root of Non-Perfect Cubes?
We cannot find the cube root of numbers which are not perfect cube using the prime factorization and estimation method. Hence, we will use here some other method.
Let us find the cube root of 30 here. Here, 30 is not a perfect cube.
Step 1:
Now we would see 30 lies between 27 ( the cube of 3) and 64 (the cube of 4). So, we will consider the lower number here, i.e. 3.
Step 2:
Divide 30 by square of 3, i.e., 30/9 = 3.33
Step 3:
Now subtract 3 from 3.33 (whichever is greater) and divide it by 3. So,
3.33 - 3 = 0.33 & 0.33/3 = 0.11
Step 4:
At the final step, we have to add the lower number which we got at the first step and the decimal number obtained.
So, 3 + 0.11 = 3.11
Therefore, the cube root of 30 is ∛30 = 3.11
This is not an accurate value but closer to it.
Let us find the cube root of 1 to 30 natural numbers
Cube Root of 1 to 30
The cube root from 1 to 30 will help students to solve mathematical problems. A list of cubic roots of numbers from 1 to 30 is provided herein a tabular format. The cube root has many applications in Maths, especially in geometry where we find the volume of different solid shapes, measured in cubic units. It will help us to find the dimensions of solids. For example, a cube has volume ‘x’ cubic meter, then we can find the side-length of the cube by evaluating the cube root of its volume, i.e., side = ∛x. Let us see the values of cubic roots of numbers from 1 to 30.
Solved Examples
Example 1: Solve ∛4 + ∛7.
Solution:
From the table, we can get the value of ∛4 and ∛7
∛4 = 1.587
∛7 = 1.913
Therefore,
∛4 + ∛7 = 1.587 + 1.913
= 3.5
Example 2: Evaluate the value of 4 ∛9
Solution:
We know,
∛9 = 2.080
Therefore,
4 ∛9 = 4 x 2.080
= 8.32
Quiz Time
Find the Value of:
Evaluate 3∛9 + 7
Solve ∛7 - ∛3
FAQs on Cube Root List from 1 to 30: Comprehensive Guide
1. What is a cube root, and how does it relate to a perfect cube?
A cube root of a number is a value that, when multiplied by itself three times (cubed), gives the original number. For example, the cube root of 64 is 4 because 4 × 4 × 4 = 64. A perfect cube is an integer that is the cube of another integer. The list of perfect cubes helps you instantly find the cube root of those numbers.
2. What are the cubes for the integers from 1 to 30?
Knowing the cubes of integers is the first step to mastering cube roots. This list helps you quickly identify perfect cubes and find their corresponding roots for problems in your CBSE syllabus. Here are the cubes for the numbers 1 to 30:
- 1³ = 1
- 2³ = 8
- 3³ = 27
- 4³ = 64
- 5³ = 125
- 6³ = 216
- 7³ = 343
- 8³ = 512
- 9³ = 729
- 10³ = 1000
- 11³ = 1331
- 12³ = 1728
- 13³ = 2197
- 14³ = 2744
- 15³ = 3375
- 16³ = 4096
- 17³ = 4913
- 18³ = 5832
- 19³ = 6859
- 20³ = 8000
- 21³ = 9261
- 22³ = 10648
- 23³ = 12167
- 24³ = 13824
- 25³ = 15625
- 26³ = 17576
- 27³ = 19683
- 28³ = 21952
- 29³ = 24389
- 30³ = 27000
3. How can we find the cube root of a number using the prime factorisation method?
The prime factorisation method is a standard technique taught in the NCERT curriculum for finding the cube root of a perfect cube. The process involves these steps:
- Step 1: Decompose the given number into its prime factors.
- Step 2: Group the identical prime factors into sets of three.
- Step 3: Select one factor from each triplet.
- Step 4: Multiply these selected factors together to obtain the cube root.
For instance, to find the cube root of 216: 216 = 2 × 2 × 2 × 3 × 3 × 3. Grouping these gives (2 × 2 × 2) and (3 × 3 × 3). Taking one factor from each group (2 and 3) and multiplying them gives 2 × 3 = 6.
4. Why is memorising the cubes of numbers from 1 to 10 so important for finding cube roots?
Memorising the cubes from 1 to 10 is crucial for using the estimation method to find cube roots of large perfect cubes quickly. The unit digit of any perfect cube is uniquely determined by the unit digit of its root. For example, a number ending in 3 (like 343) must have a cube root ending in 7. By knowing the 1-10 cube list, you can instantly identify the last digit of the root and then estimate the first digit by seeing which two perfect cubes the number falls between.
5. What is the key difference between finding a square root and a cube root?
The primary difference between square roots and cube roots lies in the grouping of factors and how they treat negative numbers.
- Grouping of Factors: For a square root, you look for pairs of identical prime factors. For a cube root, you must find triplets of identical prime factors.
- Negative Numbers: A negative number does not have a real square root (e.g., √-9 is not real). However, every negative number has a real cube root. For example, the cube root of -27 is -3, because (-3) × (-3) × (-3) = -27.
6. Where are cube roots used in real-world examples or other math topics?
Cube roots have important applications, especially in topics related to three-dimensional geometry. The most common use is in calculating the side length of a cube when its volume is known. For example, if a cubic tank has a volume of 8 cubic meters, its side length is the cube root of 8, which is 2 meters. Cube roots also appear in physics to solve problems involving density and in higher mathematics for solving cubic equations.
7. Can a negative number have a real cube root?
Yes, absolutely. Every negative number has one real cube root, which is also a negative number. This is because multiplying three negative numbers results in a negative product. For example, the cube root of -125 is -5, since (-5) × (-5) × (-5) = 25 × (-5) = -125. This property is a key distinction from square roots, which do not have real solutions for negative numbers.
