Cube Root 1 to 30: In Mathematics, the cube root of a number refers to a number that if multiplied by itself three times then results in the original given number. For example, the cube root of 27 is 3. If 3 is multiplied three times with the same number 3, then we get 3x3x3= 27. The value of the cube root of numbers from 1 to 30 assists not only school students from Class 8 but also those students preparing for competitive examinations like SSC, Banking, Railways, etc. In this article, you will learn more about the values of cube root 1 to 30, the list and chart of cube roots from 1 to 30, methods to find out the cube roots, and solved examples.
Cube Root 1 to 30
The Cube Root 1 to 30 refers to a list of the values of cube roots of all the numbers ranging from 1 to 30. It is to be noted here that the value of cube roots can be calculated for both negative and positive numbers. The values of cube roots of numbers from 1 to 30 cover from 1 to 3.1072. While dealing with the value of cube roots of numbers from 1 to 30, only 1, 8, and 27 numbers are called the perfect cubes and the left remaining numbers from 1 to 30 are called the non-perfect cubes means that their cube root is in irrational form. In radical form, the cube root from 1 to 30 is written as ∛x and in the case of exponential form, it is written as x^(⅓).
Cube Root 1 to 30 Chart
The cube root 1 to 30 chart has several uses in mathematical calculations, especially in geometry where you need to find volumes in cubic units. It helps you to calculate the dimensions of different shapes and solids. For example, if a 3D cubic-shaped body has a volume of x cubic meters, then you can calculate the length of the sides of that body by measuring the value of the cube root of the volume of that body i.e. side = ∛x. It also makes your time-consuming long mathematical equations simpler. The value of cube roots of numbers from 1 to 30 with their 3 decimal places is listed below.
Number | Cube Root (∛) |
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 |
21 | 2.759 |
22 | 2.802 |
23 | 2.844 |
24 | 2.884 |
25 | 2.924 |
26 | 2.962 |
27 | 3.000 |
28 | 3.037 |
29 | 3.072 |
30 | 3.107 |
Cube Root 1 to 30 for Perfect Cube Numbers
In the cube roots 1 to 30, the numbers 1, 8, and 27 are considered the perfect cube numbers and the remaining numbers in the list of cube roots from 1 to 30 are called the non-perfect cube numbers. The following table explains the values of cube roots from 1 to 30 for perfect cube numbers.
Cube Root 1 to 30 for Perfect Cube Numbers | |
∛1 = 1 | ∛8 = 2 |
∛27 = 3 |
Cube Root 1 to 30 for Non-Perfect Cube Numbers
Excluding the numbers 1, 8, and 27, all numbers ranging from 1 to 30 are considered non-perfect cube numbers (their cube root are in the irrational form). The following table explains the values of cube roots from 1 to 30 for non-perfect cube numbers.
Cube Root 1 to 30 for Non-Perfect Cube Numbers | ∛2 = 1.259 |
∛3 = 1.442 | ∛4 = 1.587 |
∛5 = 1.710 | ∛6 = 1.817 |
∛7 = 1.913 | ∛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 | ∛21 = 2.759 |
∛22 = 2.802 | ∛23 = 2.844 |
∛24 = 2.884 | ∛25 = 2.924 |
∛26 = 2.962 | ∛28 = 3.037 |
∛29 = 3.072 | ∛30 = 3.107 |
How to Find Cube Root from 1 to 30?
Mainly the method of the prime factorization has been mentioned below for calculating the values of cube roots from 1 to 30.
Prime Factorization
Question: Find the value of ∛27
Solution: First of all take the factors of the given number,
As per the method of the Prime factorization, 27 is 3 × 3 × 3
Now consider the pairing of resulting prime factors with the 3 combinations then we get 3.
Hence the value of ∛27 = 3
Cube Root 1 to 30 Solved Questions
Question 1: A cubic cupboard has a volume of 12 cubic inches. Calculate the length of the side of that cupboard.
Solution: As we know the volume of the cube (V) = a³ Where a is the side of the cube.
Given that the volume of the cupboard V = 12 cubic inches
So V = a³ = 12
a = ∛12 = 2.289 inches
Hence the length of the side of the cupboard is 2.289 inches.
Question 2: Calculate the cube root of the given equation 5x³ = 85.
Solution: Given that 5x³ = 85
After the division on both sides by 5,
x³ = 17
X = ∛17
Applying the values from 1 to 30 cube root chart,
The real root for the equation 5x³ = 85 is for x = 2.571
Question 3: Calculate the value of 5∛7 + ∛28
Solution: By putting the value of cube roots of 7 and 28,
5∛7 + ∛28 = 5 × (1.913) + 3.037
Hence, 5∛7 + ∛28 = 12.602
Question 4: Calculate the value of 7∛4 + 12∛29
Solution: By putting the value of cube roots of 4 and 29,
7∛4 + 12∛29 = 7 × (1.587) + 12 × (3.072)
Hence, 7∛4 + 12∛29 = 11.109 + 36.864 = 47.973
Question 5: Calculate the value of 9∛8 + 16∛1
Solution: By putting the value of cube roots of 8 and 1,
9∛8 + 16∛1 = 9 × (2) + 16 × (1)
Hence, 9∛8 + 16∛1 = 18 + 16 = 34