Properties of Cubes of Numbers
Properties of Cubes of Numbers
The cube of natural numbers have the following interesting properties:
Property 1: Cubes of all even natural numbers are even.
Property 2: Cubes of all odd natural numbers are odd.
Property 3: The sum of the cubes of first n natural numbers is equal to the square of their sum. That is,
Property 4: Cubes of the numbers ending in digits 1, 4, 5, 6, and 9 are the numbers ending in the same digit. Cubes of numbers ending in digit 2 end in digit 8 and the cube of numbers ending in digit 8 ends in digit 2. The cubes of the numbers ending in digits 3 and 7 ends in digits 7 and 3 respectively.
Explanation: The cubes of the first 10 natural numbers are given in the following table.
| Number x | Cube |
Number x | Cube |
| 1 | 1 | 11 | 1331 |
| 2 | 8 | 12 | 1728 |
| 3 | 27 | 13 | 2197 |
| 4 | 64 | 14 | 2744 |
| 5 | 125 | 15 | 3375 |
| 6 | 216 | 16 | 4096 |
| 7 | 343 | 17 | 4913 |
| 8 | 512 | 18 | 5832 |
| 9 | 729 | 19 | 6059 |
| 10 | 1000 | 20 | 8000 |
We shall learn about the cubes of negative integers.
We have,
is the cube of itself.
Similarly,
is the cube of -2.
is the cube of -3 and so on.
In general, if m is a positive integer, then
Thus, for any positive integer is the cube of -m.
Cube of a Rational Number
Let be a rational number (m, n are non-zero integers such that
) other than an integer, then the cube of a is defined as
or,
The unit's digit of the cube of a number is 9. The unit's digit of its cube root is ______ . | |||
| Right Option : A | |||
| View Explanation | |||
Calculate the value of | |||
| Right Option : C | |||
| View Explanation | |||
Mr. X gave a problem to Mr. Y. " Difference of two perfect cubes is 189. If the cube root of the smaller of the two number is 3, find the cube root of the larger number. " Help Mr. Y to answer the question. | |||
| Right Option : B | |||
| View Explanation | |||
Students / Parents Reviews [10]
A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thAbhyas 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.
Manish Kumar
10thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thIt 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.
Cheshta
10thBeing 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.
Prisha Gupta
8thIt 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.
Eshan Arora
8thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thMy 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.
Shivam Rana
7thAbhyas 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.
Om Umang
10thOne 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.
