Find which of the following are perfect cubes?

(i) 243

(ii) 588

(iii) 1331

(iv) 24000

(v) 1728

(vi) 1938

(i) 243
Finding prime factors of 243

243 = (3 x 3 x 3) x 3 x 3

Since the prime factor 3 is not in triplets,

Hence, 243 is not a perfect cube.

(ii) 588
Finding prime factors of 588

588 = 2 x 2 x 3 x 7 x 7

Since the prime factor 2, 3 and 7 are not in triplets,

Hence, 588 is not a perfect cube.

(iii) 1331
Finding prime factors of 1331

1331 = (11 x 11 x 11)

Since the prime factor 11 forms a triplet,

Hence, 1331 is a perfect cube.

(iv) 24000
Finding prime factors of 24000

24000 = (2 x 2 x 2) x (2 x 2 x 2) x 3 x (5 x 5 x 5)

Since the prime factor 3 is not in triplets,

Hence, 24000 is not a perfect cube.

(v) 1728
Finding prime factors of 1728

1728 = (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3)

Since the prime factor 2 and 3 are in triplets,

Hence, 1728 is a perfect cube.

(vi) 1938
Finding prime factors of 1938

1938 = 2 x 3 x 17 x 19

Since the prime factor 2, 3, 17 and 19 are not in triplets,

Hence, 1938 is not a perfect cube.