Using prime factorisation, find which of the following are perfect cubes.

(a) 128 (b) 343

(c) 729 (d) 1331

(a) Given: 128

Factors of 128 = 2 ×2 × 2×2×2×2×2

= 2³ × 2³×2

As we see, 128 is not a perfect cube.

(b) Given: 343

Factors of 343 = 7 × 7 × 7

= 7³

So, 343 is a perfect cube.

(c) Given: 729

Factors of 729 = 3 × 3 × 3 × 3 × 3 × 3

= 3³× 3³

So, 729 is a perfect cube.

(d) Given: 1331

Factors of 1331 = 11 × 11 × 11

= 11³

So, 1331 is a perfect cube.