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Question

Find the cube root by prime factorization:

(i) 10648; (ii) 46656; (iii) 15625.

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Solution

(i) 10648

= 2 × 5324

= 2 × 2 × 2662

= 2 × 2 × 2 × 1331

= 2 × 2 × 2 × 11 × 121

= 2 × 2 × 2 × 11 × 11 × 11

(ii) 46656

= 2 × 23328

= 2 × 2 × 11664

= 2 × 2 × 2 × 5832

= 2 × 2 × 2 × 2 × 2916

= 2 × 2 × 2 × 2 × 2 × 1458

= 2 × 2 × 2 × 2 × 2 × 2 × 729

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 243

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

(iii) 15625

= 5 × 3125

= 5 × 5 × 625

= 5 × 5 × 5 × 5 × 5 × 5


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