Question 15 Marks
Which of the following are cubes of an odd number $.216, 729, 3375, 8000, 125, 343, 4096$ and $9261.$
Answer
View full question & answer→$\because 216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3$
$= (2)^3 \times (3)^3$
$= (6)^{3}$
$\because 729 ={ 3 \times 3 \times 3 \times 3 \times 3 \times 3}$
$= (3)^3 \times (3)^3$
$= (9)^{3}$
$\because 3375 = {5 \times 5 \times 5 \times 3 \times 3 \times 3}$
$= (5)^3 \times (3)^3$
$= (15)^3$
$\because 8000 = 20 \times 20 \times 20$
$= (20)^3$
$125 = 5 \times 5 \times 5$
$= (5)^3$
$\because 343 = 7 \times 7 \times 7$
$= (7)^3$
$\because 4096 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= (2)^3 \times (2)^3 \times (2)^3 \times (2)^3$
$=(16)^3$
Cubes of an odd number are $729, 3375, 125, 343, 9261.$
| $2$ | $216$ |
| $2$ | $108$ |
| $2$ | $54$ |
| $3$ | $27$ |
| $3$ | $9$ |
| $3$ | $3$ |
| $1$ |
$= (6)^{3}$
$\because 729 ={ 3 \times 3 \times 3 \times 3 \times 3 \times 3}$
| $3$ | $729$ |
| $3$ | $243$ |
| $3$ | $81$ |
| $3$ | $27$ |
| $3$ | $9$ |
| $3$ | $3$ |
| $1$ |
$= (9)^{3}$
$\because 3375 = {5 \times 5 \times 5 \times 3 \times 3 \times 3}$
| $5$ | $3375$ |
| $5$ | $675$ |
| $5$ | $135$ |
| $3$ | $27$ |
| $3$ | $9$ |
| $3$ | $3$ |
| $1$ |
$= (15)^3$
$\because 8000 = 20 \times 20 \times 20$
$= (20)^3$
| $5$ | $125$ |
| $5$ | $25$ |
| $5$ | $5$ |
| $1$ |
$= (5)^3$
$\because 343 = 7 \times 7 \times 7$
$= (7)^3$
| $7$ | $343$ |
| $7$ | $49$ |
| $7$ | $7$ |
| $1$ |
| $2$ | $4096$ |
| $2$ | $2048$ |
| $2$ | $1024$ |
| $2$ | $512$ |
| $2$ | $256$ |
| $2$ | $128$ |
| $2$ | $64$ |
| $2$ | $32$ |
| $2$ | $16$ |
| $2$ | $8$ |
| $2$ | $4$ |
| $2$ | $2$ |
| $1$ |
$=(16)^3$
Cubes of an odd number are $729, 3375, 125, 343, 9261.$