Answer
64.8k+ views
Hint: Here, we will first take the cube of few of the natural numbers and then find out if the obtained cubes are equal to the natural number itself to find the required value.
Complete step-by-step solution:
Given that the number is a natural number.
We know that the natural numbers are a part of the number system, which includes all the positive integers from 1 till infinity, which is denoted by the symbol, \[\infty \].
Now we will find the cube of some of the natural numbers to find the required value.
First, we will find the cube of the natural number 1.
\[
{1^3} = 1 \times 1 \times 1 \\
= 1 \\
\]
Since we have seen from above that the cube of the natural number 1 is 1, so 1 is the required natural number whose cube is equal to itself.
We will also find the cube of some other natural number for the accuracy of our answer.
Finding the cube of the natural number 2, we get
\[
{2^3} = 2 \times 2 \times 2 \\
= 8 \\
\]
As this natural number 2 is not equal to its cube, the natural number 2 is not the required value.
Finding the cube of the natural number 3, we get
\[
{3^3} = 3 \times 3 \times 3 \\
= 27 \\
\]
Since this natural number 3 is also not equal to its cube, so the natural number 3 is also not the required value.
We will also take some larger natural number randomly and find its cube.
Let us take the number 7.
We will now find the cube the natural number 7.
\[
{7^3} = 7 \times 7 \times 7 \\
= 343 \\
\]
Again we have seen that this natural number is also not equals to its cube.
Continuing like the above, we will find out that 1 is the only natural number whose cube is equal to itself.
Therefore, the natural number whose cube is equals to itself be 1.
Note: In solving these types of questions, you should be familiar with the concept of natural numbers. Students should also take the cube of some other natural numbers carefully for more accuracy. Then use the given conditions and values given in the question, to find the required values. Also, we are supposed to write the values properly to avoid any miscalculation.
Complete step-by-step solution:
Given that the number is a natural number.
We know that the natural numbers are a part of the number system, which includes all the positive integers from 1 till infinity, which is denoted by the symbol, \[\infty \].
Now we will find the cube of some of the natural numbers to find the required value.
First, we will find the cube of the natural number 1.
\[
{1^3} = 1 \times 1 \times 1 \\
= 1 \\
\]
Since we have seen from above that the cube of the natural number 1 is 1, so 1 is the required natural number whose cube is equal to itself.
We will also find the cube of some other natural number for the accuracy of our answer.
Finding the cube of the natural number 2, we get
\[
{2^3} = 2 \times 2 \times 2 \\
= 8 \\
\]
As this natural number 2 is not equal to its cube, the natural number 2 is not the required value.
Finding the cube of the natural number 3, we get
\[
{3^3} = 3 \times 3 \times 3 \\
= 27 \\
\]
Since this natural number 3 is also not equal to its cube, so the natural number 3 is also not the required value.
We will also take some larger natural number randomly and find its cube.
Let us take the number 7.
We will now find the cube the natural number 7.
\[
{7^3} = 7 \times 7 \times 7 \\
= 343 \\
\]
Again we have seen that this natural number is also not equals to its cube.
Continuing like the above, we will find out that 1 is the only natural number whose cube is equal to itself.
Therefore, the natural number whose cube is equals to itself be 1.
Note: In solving these types of questions, you should be familiar with the concept of natural numbers. Students should also take the cube of some other natural numbers carefully for more accuracy. Then use the given conditions and values given in the question, to find the required values. Also, we are supposed to write the values properly to avoid any miscalculation.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)