Cube Root 1 to 30: Steps to Calculate with Examples

Cube of a number is its multiplication by itself three times and the cube root is just the inverse of it. The cube root of a number is the opposite function of its cube. For example, if the cube of any number is a³ then its cube root will be a.

The cube root is a widely used concept in Mathematics, especially in geometry, where volumes of various shapes have cubic units. 

Also Read: Cube and Cube Roots

Key Terms: Cube, Cube Root, Integer, Geometry, Prime Factorisation, Square Root

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What is Cube Root?

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The cube root of a number a is a number that when multiplied thrice by itself gives the same number a. 

• It is simply the inverse operation of a cube. 
• The cube root of a number is just the opposite of cubing of that number. 
• The cube root is denoted by the symbol ∛ which is just the “radical” symbol, which is used for the square root, with a little 3 over it. 

For a perfect cube x of any integer y i.e., x = y³, then y is called the cube root of x and it is denoted by y = ∛x.

Cube Root

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Cube Root of Non-perfect Cubes

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It is easier to find the cube root of numbers which are perfect cubes but for non-perfect cubes, we use the prime factorisation method. The steps to find the cube root of a non-perfect cube, 30, are as follows.

• Since we know 30 lies between 27 which is a cube of 27 and 64 the cube of 4. So, let’s consider the lower number here, i.e. 3.
• Dividing 30 by the square of 3: 30/9 = 3.33 
• Subtracting 3 from 3.33 and then dividing it by 3. 
• 3.33 - 3 = 0.33 & 0.33/3 = 0.11
• The final step is to add the lower number which we got in the first step and the decimal number obtained.
•  3 + 0.11 = 3.11

Therefore, the cube root of 30 is ∛30 = 3.11

Also Read: Decimal to Fraction Formula

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Cube Root of 1 to 30

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The cube root of 1 to 30 is used very commonly and for that purpose, a table is given below.

Also Read: Number System

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Solved Examples

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To understand better the concept of the cube root a few examples are given below.

Example 1: Solve ∛30 – 3.

Solution: Here, we have

∛30 = 3.1072

Thus,

∛30 – 3 = 3.1072 – 3 = 0.1072

Example 2: Solve ∛5 + ∛8.

Solution: Taking the value of ∛5 and ∛8 from the table given above

∛5 = 1.70997.. = 1.71 

∛8 = 2

Thus,

∛5 + ∛8 = 1.71+2 = 3.71

Also Read:

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Things to Remember

• The cube root of a number is the opposite of its cube function.
• Cube root of non-perfect numbers is found through the prime factorization method.
• The cube root of unity is unity.
• The symbol of cube root is ∛.
• Cube root of perfect cubes are integers but of non-perfect cubes, it will be a decimal.