Question

Which of the following numbers are not perfect cubes?

(i) 64

(ii) 216

(iii) 243

(iv) 1728

Answer 1

(i) 64

64 = 2 × 2 × 2 × 2 × 2 × 2

= 2³ × 2³

= 4³

Hence, it’s a perfect cube.

(ii) 216

216 = 2 × 2 × 2 × 3 × 3 × 3

= 2³ × 3³

= 6³

Hence, it’s a perfect cube.

(iii) 243

243 = 3 × 3 × 3 × 3 × 3

= 3³ × 3²

Hence, it’s not a perfect cube.

(iv) 1728

1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

= 2³ × 2³ × 3³

= 12³

Hence, it’s a perfect cube.