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Question:

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: (i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704

Solution:

(i) 81 = 3 × 3 × 3 × 3 = 3³ × 3
Required number = 3
(ii) 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2³ × 2³ × 2
Required number = 2
(iii) 135 = 3 × 3 × 3 × 5 = 3³ × 5
Required number = 5
(iv) 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2³ × 2³ × 3
Required number = 3
(v) 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11 = 2³ × 2³ × 11
Required number = 11