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 : A | |||
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| Right Option : C | |||
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Given that | |||
| Right Option : D | |||
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Students / Parents Reviews [20]
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.
Shivam Rana
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Ayan Ghosh
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Om Umang
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