Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100
(i) We have 243 = 3 x 3 x 3 x 3 x 3 or, 729, = 3 x 3 x 3 x 3 x 3 x 3 ∴ The smallest number required to multiply 72 to make it a perfect cube is 3. (iv) We have 675 = 3 x 3 x 3 x 5 x 5Grouping the prime factors of 675 to triples, we are left over with 5 x 5 |