Question

Write property of cube ??

Answer 1

Properties of Cube

Some properties of cubes of natural numbers are:- 

Property 1: Cubes of all even numbers are even. 
Example: 63 = 6 x 6 x 6 = 216 
6 and 216 both are even numbers.

Property 2: Cubes of all odd natural numbers are odd. 
Example: 73 = 7 x 7 x 7 = 343
7 and 343 both are natural odd numbers.

Property 3: The sum of the cubes of first n natural numbers is equal to the square of their sum. 
13 + 2 3 + 33 + … + n3 = (1 + 2 + 3 + … + n)2 
Example: 13 + 23 + 33 + 43 = (1 + 2 + 3 + 4)3 
1 + 8 + 27 + 64 = (10)2 
100 = 100 

Property 4 : Cubes of the numbers ending in digit 1, 4, 5, 6 and 9 are the numbers ending in the same digit.






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Answer 2

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SOME PROPERTIES OF CUBE

 Property 1 : 

For numbers with their unit’s digit as 1, their cubes also will have the unit’s digit as 1.

For example,

1³  =  1

11³  =  1331

21³  =  9261

31³  =  29791

Property 2 :

The cubes of the numbers with 1, 4, 5, 6, 9 and 0 as unit digits will have the same unit digits.

For example, 

14³  =  2744

15³  =  3375

16³  =  4096

20³  =  8000

Property 3 :

The cube of numbers ending in unit digit 2 will have a unit digit 8 and the cube of the numbers ending in unit digit 8 will have a unit digit 2.

For example, 

12³  =  1728

18³  =  5832

Property 4 :

The cube of the numbers with unit digits as 3 will have a unit digit 7 and the cube of numbers with unit digit 7 will have a unit digit 3.

For example, 

13³  =  2197

27³  =  19683

Property 5 :

The cubes of even numbers are all even; and the cubes of odd numbers are all odd.

For example, 

18³  =  5832 (even)

27³  =  19683 (odd) 

Property 6 :

The sum of the cubes of first n natural numbers is equal to the square of their sum. 

That is,

1³ + 2³ + 3³ + ....... + n³  =  (1 + 2 + 3 + ..... + n)²

For example,

1³ + 2³ + 3³ + 4³  =  (1 + 2 + 3 + 4)²

1 + 8 + 27 + 64  =  (10)²

100  =  100



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