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What is the smallest number by which the following numbers must be multiplied, so that the products are perfect cubes? (i) 675 (ii) 1323 (iii) 2560 (iv) 7803 (v) 107811 (vi) 35721 |
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Answer» (i) 675 Factors of 675 = 3 × 3 × 3 × 5 × 5 = 33 × 52 Hence, to make a perfect cube we need to multiply the product by 5. (ii) 1323 Factors of 1323 = 3 × 3 × 3 × 7 × 7 = 33 × 72 Hence, to make a perfect cube we need to multiply the product by 7. (iii) 2560 Factors of 2560 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 = 23 × 23 × 23 × 5 Hence, to make a perfect cube we need to multiply the product by 5 × 5 = 25. (iv) 7803 Factors of 7803 = 3 × 3 × 3 × 17 × 17 = 33 × 172 Hence, to make a perfect cube we need to multiply the product by 17. (v) 107811 Factors of 107811 = 3 × 3 × 3 × 3 × 11 × 11 × 11 = 33 × 3 × 113 Hence, to make a perfect cube we need to multiply the product by 3 × 3 = 9. (vi) 35721 Factors of 35721 = 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7 = 3 3 × 3 3 × 72 Hence, to make a perfect cube we need to multiply the product by 7. |
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