Question

Find the cube root of each of the following rational numbers:

(i) -125/729

(ii) 10648/12167

(iii) -19683/24389

Answer 1

(i) -125/729

-125/729 = – (∛ (5×5×5)) / (∛ (9×9×9))

= – (∛(53)) / (∛(93))

= – 5/9

(ii) 10648/12167

10648/12167 = (∛ (2×2×2×11×11×11)) / (∛(23×23×23))

= (∛ (2³×11³)) / (∛(23³))

= (2×11)/23

= 22/23

(iii) -19683/24389

-19683/24389 = -(∛(3×3×3×3×3×3×3×3×3)) / (∛(29×29×29))

= – (∛(3³×3³×3³)) / (∛(29³))

= – (3×3×3)/29

= – 27/29