Question

Find the cube roots of the numbers 3048625, 20346417, 210644875, 57066625 using the fact that

(i) 3048625 = 3375 × 729

(ii) 20346417 = 9261 × 2197

Answer 1

(i) 3048625 = 3375 × 729

∛3048625 = ∛3375 × ∛729

= ∛3×3×3×5×5×5 × ∛9×9×9

= ∛3³×5³ × ∛9³

= 3×5×9

= 135

(ii) 20346417 = 9261 × 219

∛20346417 = ∛9261 × ∛2197

= ∛3×3×3×7×7×7 × ∛13×13×13

= ∛3³×7³ × ∛13³

= 3×7×13

= 273