hlo mates properties of cube of numbers
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Properties of Perfect Cubes. The cubes of numbers with counting digits, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 as the unit's digits end with 0, 1, 8, 7, 4, 5, 6, 3, 2, and 9 respectively.
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Property 1: Cubes of all even numbers are even.
Example: 6 3 = 6 x 6 x 6 = 216
6 and 216 both are even numbers.
Property 2: Cubes of all odd natural numbers are odd.
Example: 7 3 = 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.
1 3 + 2 3 + 3 3 + … + n 3 = (1 + 2 + 3 + … + n) 2
Example: 1 3 + 2 3 + 3 3 + 4 3 = (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.
Numbers
Property 1: Cubes of all even numbers are even.
Example: 6 3 = 6 x 6 x 6 = 216
6 and 216 both are even numbers.
Property 2: Cubes of all odd natural numbers are odd.
Example: 7 3 = 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.
1 3 + 2 3 + 3 3 + … + n 3 = (1 + 2 + 3 + … + n) 2
Example: 1 3 + 2 3 + 3 3 + 4 3 = (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.