Which of the following numbers are not perfect cubes?
(i) 64
(ii) 216
(iii) 243
(iv) 1728
(i) 64
Prime factors of 64 = 2 × 2 × 2 × 2 × 2 × 2 = 23 × 23 = 43
Hence, it’s a perfect cube.
(ii) 216
Prime factors of 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33 = 63
Hence, it’s a perfect cube.
(iii) 243
Prime factors of 243 = 3 × 3 × 3 × 3 × 3 = 33 × 32
Hence, its not a perfect cube.
(iv) 1728
Prime factors of 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 23 × 23 × 33 = 123
Hence, it’s a perfect cube.