Question

864 is a perfect cube or not​

Answer 1

Answer:

For this just do its prime factorisation and if all are in triplets(in pair of 3) it will be a perfect cube.

Step-by-step explanation:

Look at image attached for prime factoristaion method

Now,

864= (2×2×2) in triplet form × (2×2)not in triplet form × (3×3×3)in triplet form

Now we can see that middle ones are not in triplet form So it is not an Perfect cube.

ADDITIONAL

To make it a perfect cube we have to multiply 864 from 2

Because one 2 is missing in the middle factor to make it a triplet

864 × 2 = 1728

now 1728 is a perfect cube

Its factors are

1728= (2×2×2) × (2×2×2) × (3×3×3) ----(1)

all are in triplet form so it is a perfect cube

Of

(continuing form eq(1))

2 × 2× 3

4×3

12

checking

12 ×12×12

=144 ×12

=1728

Hence done