Cube Root 1 to 50

When multiplying a number three times gives the original number, it is known as a cube root. It is the reverse of finding the cube of a number. It is represented by the symbol ∛x, where x is the number. For example, ∛27 is 3 because by multiplying 3 by itself three times we will get the original value (27), 3 × 3 × 3 = 27.
 

Cube roots are useful for solving mathematical problems that involve volumes, especially for cubes and three-dimensional shapes. The below cube root chart shows the cube root values from 1 to 50.
 

Listing the cube roots from 1 to 50 can help kids understand and learn the values of cube roots easily. Let's learn the list of cube roots from 1 to 50.

Cube Roots from 1 to 10

The cube roots of 1 to 10 consist of perfect cubes and approximate decimal values. Go through the given list below to learn the cube roots from 1 to 10.

Cube Roots from 11 to 20
Cube roots from 11 to 20 consist of non-perfect cubes with decimal approximations. Listed below are the cube roots from 11 to 20.

Cube Root from 21 to 30
The cube roots from 21 to 30 also involve perfect cubes and decimal approximation. The list below gives the correct value for the cube roots from 21 to 30.
 

Cube Roots from 31 to 40
The numbers in cube roots from 31 to 40 include approximation. The given list has the values of cube roots from 31 to 40.
 

Cube Roots from 41 to 50
The following lists show the values of cube roots from 41 to 50.

When an integer is multiplied by itself, three times perfect cube is formed. The cube root of a perfect cube is always an integer. The perfect cubes from 1 to 50 are 1, 8, and 27.
 

When we multiply a number three times by itself, and it does not result in integers, it is a non-perfect cube. All the numbers from 1 to 50 except 1, 8, and 27 are non-perfect cubes.
 

By calculating the cube roots from 1 to 50, we use the following two methods. They are,

• By Prime Factorization Method
• By Estimation Method
   

The prime factorization method breaks down a number into its prime factors and finds the cube root. We can see clearly about this in the following steps.

Step 1: The given number is prime factorized

Step 2: List the factors and group the same factors in a group of 3

Step 3: Remove the cube root and multiply the factors. If a factor is left out that cannot be grouped, that means that is not a perfect cube. 

Let’s check the cube root of 27, 

Step 1: Prime factorization of 27 = 3 × 3 × 3

Step 2: Grouping the factors ∛(3 × 3 × 3)

Step 3: Cube root of 27 = 3 

In the estimation method, the cube root of the number is calculated by estimating the nearby perfect cubes.
Finding the cube root of 18

Step 1: We find the nearest perfect cubes 
The nearest perfect cubes of 18 are 8(2³) and 27(3²)

Step 2: Find the nearest number 
Here the nearest cube root is 8, so the cube root of 18 is near to 2.

Step 3: Estimate the value by cubing it
Checking the cube root by cubing. 2.1³ = 9.261, 2.4³ = 13.824, 2.6³ = 17.576, 2.7³ = 19.683.

So, the estimated value of the cube root of 18 is 2.62

As we discussed there are different methods to find the cube root of a number. So let’s discuss some of the basic rules to find the cube root from 1 to 50.

Rule 1: Exact Cubes
The exact cube is also known as the perfect cube. A perfect cube is a number when cubed gives the number. The exact cubes from 1 to 50 are 1(1³), 8(2³), 27(3³).

Rule 2: Approximation for Non-Exact Cubes
In approximation, the cube root is calculated by estimating the nearest perfect cube. For instance, the cube root of 18 in the approximation method can be calculated by estimating the nearest perfect cubes. Here the nearest perfect cubes are 2³(8) and 3³(27), so the cube root of 18 is 2.62. 

Rule 3: Properties of Cube Roots

The cube of a negative number is always negative. That is ∛(-27 )= -3. When multiplying or dividing cube root we can split the numbers into its cube root and so the operations. For instance, ∛(27 × 8) = ∛27  × ∛8 and ∛(64 / 8) = ∛64 / ∛8.

Rule 4: Using Cube Root Formula

The formula to find the value of the cube root of a number is x = ∛y so, x = y^1/3. Which means finding the value of the cube root of 27 using the formula. Here y = 27, so x = ∛27 = 3. 

Now let’s learn a few tips and tricks for cube root 1 to 50. These tips and tricks can make the learning process easier and more interesting.

• By memorizing the perfect cubes such as 1, 8, 27, and 64.
   
• When finding the value of a non-perfect cube students can use the estimation method.
   
• The cube root follows a pattern that is 

  Unit place of the number	Unit place of the cube
  0	0
  2	8
  3	7
  4	4
  5	5
  6	6
  7	3
  8	2
  9	9

   

• Perfect cube: Perfect cube is a number which can be expressed as a cube of the number. 

• Prime factorization: The way of writing number as the product its prime factors.

• Volume: The area occupied by an object in a three dimension space