Cube root of 1 to 20 – definition, values, and FAQs

Before we get into the value of the cube root from 1 to 20, let us understand what a cube root is and how to calculate the cube roots of a perfect cube. A cube is a value we get when we multiply a number by itself three times. 

For example, 3^{3}=3 \times 3 \times 3=27 . \text { So, } 27 \text { is the cube of } 3

The cube root of a number is the value which when multiplied by itself three times, gives the original number. 

For example, the cube root of 27, denoted as ∛27, is 3 i.e. the number which when multiplied by itself three times gives 27. 

So, 27 is the cube of 3, and 3 is the cube root of 27.

In this article let us understand how to calculate the cube roots of perfect cubes, how to calculate the cube roots using the simple calculator, and the value of the cube roots of the numbers 1-20. 

Value of the cube root of 1 to 20 :

It is recommended to memorize the cubes and cube roots of 1 to 20 as it would help the students to solve complex mathematical sums faster and easier.  Cube roots are largely used in mensuration problems where the students are expected to find the length of a side and the volume of the object is given. The value of the cube roots of 1 to 20 is given here for the student’s reference. 

Prime factorization for calculating cube root:

We can calculate the cube root of a perfect cube using prime factorization with relative ease. Let us understand this method with the help of an example. 

Let us calculate the cube root of 3375.

Step – 1: Let us list out the prime factors of 3375 using the prime factorization method.

Listing out the factors, we get 3375 = 3 ✕ 3 ✕ 3 ✕ 5 ✕ 5 ✕ 5 

Step – 2: Consider the prime factor once every three times it is repeated. Thus, we get

3 ✕ 5 = 15 as the cube root. 

Solved Illustrations:

1. Calculate the cube root of 729 using the prime factorization method.

Solution:

Listing out the prime factors of 729, we get 729 = 3 ✕ 3 ✕ 3 ✕ 3 ✕ 3 ✕ 3.

Next, we shall Consider the prime factor once every three times it is repeated. Since 3 is repeated 6 times, we get 3 ✕ 3 = 9 as the cube root of 729.

2. Find the value of \sqrt[3]{12}+12^{3}.

Solution:

From the above table, we know that the value of ∛12 = 2.289.

So, the value of \sqrt[3]{12}+12^{3} \text { is } 2.289+1728=1730.289

3. If the volume of a cube is 15 m³, find the length of the cube

Solution:

We know that the volume of a cube =a^{3} where a is the length of the cube. 

\text { So, } 15 {\text{m}}^{3}=a^{3}

a=\sqrt[3]{15}

a = 2.466 m