Question

Find which of the following numbers are cubes of rational numbers:

(i) 27/64

(ii) 125/128

(iii) 0.001331

(iv) 0.04

Answer 1

(i) 27/64

27/64 = (3×3×3)/ (4×4×4) 

= 3³/4³

 = (3/4)³

= 27/64 

(ii) 125/128

125/128 = (5×5×5)/ (2×2×2×2×2×2×2) 

= 5³/ (2³×2³×²)

= 125/128 is not a perfect cube.

(iii) 0.001331 

1331/1000000 = (11×11×11)/ (100×100×100) 

= 11³/100³ 

= (11/100)³

= 0.001331

(iv) 0.04

4/10 = (2×2)/(2×5)

 = 2²/(2×5)

= 0.04 is not a perfect cube.