Perfect Cube
Perfect Cube
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
Given that | |||
| Right Option : D | |||
| View Explanation | |||
The value of | |||
| Right Option : B | |||
| View Explanation | |||
Three numbers are in the ratio 2 : 3 : 5 to one another. The sum of their cubes is 54880. The numbers are _____ . | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [20]
My 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.
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Barkha Arora
10thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
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Cheshta
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8thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
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8thA 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.
