Question

Which of the following are cubes of an odd number

216, 729, 3375, 8000, 125, 343, 4096 and 9261.

Answer 1

∵ 216 = 2 x 2 x 2 x 3 x 3 x 3

2	216
2	108
2	54
3	27
3	9
3	3
	1

 

 

 

 

 

 

 

= (2)³ x (3)³
= (6)³

∵ 729 = 3 x 3 x 3 x 3 x 3 x 3

3	729
3	243
3	81
3	27
3	9
3	3
	1

 

 

 

 

 

 

 

= (3)³ x (3)³
= (9)³

∵ 3375 = 5 x 5 x 5 x 3 x 3 x 3

5	3375
5	675
5	135
3	27
3	9
3	3
	1

 

 

 

 

 

 

 

= (5)³ x (3)³
= (15)³

∵ 8000 = 20 x 20 x 20
= (20)³

5	125
5	25
5	5
	1

 

 

 

 

125 = 5 x 5 x 5
= (5)³

∵ 343 = 7 x 7 x 7
= (7)³

7	343
7	49
7	7
	1

 

 

 

 

∵ 4096 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

2	4096
2	2048
2	1024
2	512
2	256
2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

 

 

 

 

 

 

 

 

 

 

 

 

 

= (2)³ x (2)³ x (2)³ x (2)³
=(16)³

Cubes of an odd number are 729, 3375, 125, 343, 9261.