Question

Why is 4000 not a perfect cube, whereas 8000 and 1000 are perfect cubes

Answer 1

Answer:

a perfect cube is one which is equally divisible by a number three times

8000 is 20*20*20  so it is a perfect cube

1000 is 10*10*10 which is also a perfect cube

but if we divide 4000, we get 2*2*10*10*10

there are only two 2s so we cannot call it a perfect cube

for it to be be a perfect cube it should have been 2*2*2*10*10*10

which is 8000

Answer 2

SOLUTION –

Factors of 4000

= 10×10×10 × 2×2

---------------- ------

Here, 2 doesn't form a triplets .

Therefore, 4000 is not a perfect cube .

Again , Factors of 8000

=10×10×10 × 2×2×2

--------------- ----------

Here , all factors have a triplets .

Therefore , 8000 is a perfect cube .

Again , factors of 1000

= 10×10×10

---------------

Here , all factors have a triplets .

Therefore , 1000 is a perfect cube .

HENCE , 4000 is not a perfect cube whereas 8000 and 1000 is a perfect cube.