How to Find Cube Roots from 1 to 30 with Formula and Examples
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 Roots from 1 to 30 Complete Table
1. What is the cube root list from 1 to 30?
The cube root list from 1 to 30 includes the cube roots of natural numbers 1 through 30, showing which are perfect cubes and which are irrational values.
- ∛1 = 1
- ∛8 = 2
- ∛27 = 3
2. What are the perfect cube numbers between 1 and 30?
The perfect cubes between 1 and 30 are numbers whose cube roots are whole numbers.
- 1 = 1³
- 8 = 2³
- 27 = 3³
3. What is the cube root of 2 to 30 in decimal form?
The cube roots of numbers from 2 to 30 (non-perfect cubes) are irrational and expressed in decimals.
- ∛2 ≈ 1.26
- ∛3 ≈ 1.44
- ∛4 ≈ 1.59
- ∛5 ≈ 1.71
- ∛6 ≈ 1.82
- ∛7 ≈ 1.91
- ∛9 ≈ 2.08
- ∛10 ≈ 2.15
- ∛16 ≈ 2.52
- ∛25 ≈ 2.92
- ∛30 ≈ 3.11
4. How do you find the cube root of a number between 1 and 30?
The cube root of a number is found by determining the value which, when multiplied three times by itself, gives the original number.
- Step 1: Check if the number is a perfect cube (1, 8, 27).
- Step 2: If not, use prime factorization or a calculator.
- Step 3: Express the result in simplified radical or decimal form.
5. What is the formula for cube root?
The formula for cube root is ∛x = x^(1/3), which represents the number that when cubed equals x.
- If a³ = x, then ∛x = a.
- Example: 3³ = 27, so ∛27 = 3.
6. Why are only 1, 8, and 27 perfect cubes up to 30?
Only 1, 8, and 27 are perfect cubes up to 30 because they are the cubes of whole numbers 1, 2, and 3 respectively.
- 1³ = 1
- 2³ = 8
- 3³ = 27
- 4³ = 64 (which is greater than 30)
7. What is the difference between a square root and a cube root?
The difference between a square root and a cube root is that a square root multiplies a number twice, while a cube root multiplies it three times.
- Square root: √x where a² = x
- Cube root: ∛x where a³ = x
- Example: √9 = 3, but ∛9 ≈ 2.08
8. Is the cube root of numbers between 1 and 30 always positive?
The cube root of positive numbers from 1 to 30 is always positive because the cube of a positive number remains positive.
- ∛8 = 2
- ∛27 = 3
- ∛10 ≈ 2.15
9. How do you simplify cube roots between 1 and 30?
To simplify cube roots between 1 and 30, factor the number and group factors into sets of three.
- Example: ∛8 = ∛(2 × 2 × 2) = 2
- Example: ∛16 = ∛(2 × 2 × 2 × 2) = 2∛2
10. What are the uses of the cube root list from 1 to 30?
The cube root list from 1 to 30 is used to quickly identify perfect cubes and estimate cube root values in maths problems.
- Helps in simplifying radical expressions
- Useful in algebra and exponent rules
- Supports solving volume and geometry problems
- Improves mental math and number sense
