Cube of a number: When we multiply a number three times by itself, then the number is said to be cubed, and the product is called the cube of that number or the number raised to the power of 3.
In general, the cube of a number
For example,
Cube of 1 =
Cube of 2 =
Cube of 3 =
and so on.
Using the general formula, the cubes of the first 15 natural numbers are written in the following table
Number | Cube | Number | Cube | Number | Cube |
1 | 1 | 6 | 216 | 11 | 1331 |
2 | 8 | 7 | 343 | 12 | 1728 |
3 | 27 | 8 | 512 | 13 | 2197 |
4 | 64 | 9 | 729 | 14 | 2744 |
5 | 125 | 10 | 1000 | 15 | 3375 |
From this table, it is clear that 1,8,27,64,...,3375 are the cubes of some natural numbers. Such numbers are called perfect cubes.
Perfect Cube: A natural number n is a perfect cube if there exist a natural number m such that:
Or
Hence, a natural number that can be expressed as a product of triplets of equal factors is known as a perfect cube.
Cube Root: As we know, the square root is the opposite of a square. In the same way, the cube root is the opposite of a cube. For example,
Cube of 8 =
Cube root of 512 = 8
Cube of 7 =
Cube root of 343 = 7
In general, the cube of and the cube root of
is x. For any number x, the cube root is denoted by
.
Hence and
The length of each edge of a cube is 9 m. The volume of the cube, in | |||
Right Option : D | |||
View Explanation |
Which one of the following numbers is not a complete cube? 64, 216, 343, 256 | |||
Right Option : D | |||
View Explanation |
The value of | |||
Right Option : B | |||
View Explanation |
My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.