Question

Properties of perfect cube​

Answer 1

$\underline\mathfrak{Properties}$

1. The cube of an even number is always even. Example- 2×2×2=8
2. Cube of an odd number is always odd. Example- 3×3×3=27
3. If we calculate the cubes of numbers ending in 0,1,4,5,6,9 we obtain the numbers ending in the same digit. Example- 9×9×9=729
4. Sum of first n successive natural numbers cube is same as the whole square of their sum. Example-
5. ${1}^{3} + {2}^{3} + {3}^{3}$

= 1+8+27 = 36

$(1 + 2 + 3 {)}^{2}$

$= {6}^{2}$

= 36

6.The cube of a rational number is equal to the cube of the denominator and numerator separately. Example-

$(\frac{5 }{6 } {)}^{3} = \frac{ {5}^{3} }{ {6}^{3} } = \frac{125}{216}$