Question

Which of the following are cubes of :

(i) an even number

(ii) an odd number

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

Answer 1

$\because 216=2\times 2\times 2\times 3\times 3\times 3$

$=(2{)}^3\times (3{)}^3=(6{)}^3\because 729=3\times 3\times 3\times 3\times 3\times 3$

$=(5{)}^3\times (3{)}^3=(15{)}^3$

$\because 3375=5\times 5\times 5\times 3\times 3\times 3$

$=(5{)}^3\times (3{)}^3=(15{)}^3\because 8000=20\times 20\times 20=(20{)}^3$

$125=5\times 5\times 5=(5{)}^3$

$\because 343=7\times 7\times 7=(7{)}^3$

$\because 4096=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

$=(2{)}^3\times (2{)}^3\times (2{)}^3\times (2{)}^3=(16{)}^3$\)

(i) Cubes of an even number are 216,8000,4096.

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