Checking if perfect cube

Let’s do this by examples

Is 216 a perfect cube?

Let’s do prime factorization of 216

Thus,

 216  = 2 × 2 × 2 × 3 × 3 × 3

Now,

We make groups of 3

Since 2 & 3 occur in triplets.

∴ 216 is a perfect cube.

Cube root of 216 = 2 × 3

         = 6

Is 729 a perfect cube?

Doing Prime factorization of 729

We see that

Since 3 occurs in triplets.

∴ 729 is a perfect cube.

Cube root of 729 = 3 × 3

Is 3375 a perfect cube?

Doing Prime factorization of 3375

We see that

Since 3 & 5 occurs in triplets.

∴ 3375 is a perfect cube.

Cube root of 3375 = 3 × 5

       = 15

Is 1125 a perfect cube?

Doing Prime factorization of 1125

We see that

Since 3 does not occur in triplets

∴ 1125 is not a perfect cube.

Is 6859 a perfect cube?

Doing Prime factorization of 6859

We see that

Since 19 occurs in triplets.

∴ 6859 is a perfect cube.

Cube root of 6859 = 19

Is 10648 a perfect cube?

Doing Prime factorization of 10648

We see that

Since 2 & 11 occurs in triplets.

∴ 10648 is a perfect cube.

Cube root of 10648 = 2 × 11

        = 22

Is 5324 a perfect cube?

Doing Prime factorization of 5324

We see that

Since 2 does not occur in triplets.

∴ 5324 is not a perfect cube.

Is 968 a perfect cube?

Doing Prime factorization of 968

We see that

Since 11 does not occur in triplets.

∴ 968 is not a perfect cube

Is 400 a perfect cube?

Doing Prime factorization of 400

Since 2 & 5 do not occur in triplets.

∴ 400 is not a perfect cube.