properties of cube

# Properties of Cube

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Some properties of cubes of natural numbers are:-

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 Cubes 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000

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Practice

1) Express 8
3 as sum of odd natural numbers.
2) Find the odd numbers to be added to get the following cubes.
a) 7
3 .
b) 12
3
c) 4
3

3) State the unit digits of the cubes of the following numbers.
a) (387)
3
b) (83)
3
c) (-81)
3
d) (55)
3
e) (680)
3
Cube and Cube Roots

Cube of Numbers
Perfect Cube
Properties of Cube
Cube by Column method
Cube of Negative numbers
Cube of Rational numbers
Cube-Root
Finding cube-root by Prime Factorization
Cube root of Rational numbers
Estimating cube root

From Properties of cube to Exponents

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