mechanical properties of metals eve...
mechanical properties of metals everyone must know.

# 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: 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.
 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 83 as sum of odd natural numbers.
2) Find the odd numbers to be added to get the following cubes.
a) 73.
b) 123
c) 43

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