Properties of Cube
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.
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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
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