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Which of the following are perfect cubes?(i) 64(ii) 216 (iii) 243(iv) 1000 (v) 1728 (vi) 3087 |
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Answer» (i) 64 64 = 2 × 2 × 2 × 2 × 2 × 2 = 26 = (22)3 = 43 Hence, it’s a perfect cube. (ii) 216 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33 = 63 Hence, it’s a perfect cube. (iii) 243 243 = 3 × 3 × 3 × 3 × 3 = 35 = 33 × 32 Hence, it’s not a perfect cube. (iv) 1000 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 23 × 53 = 103 Hence, it’s a perfect cube. (v) 1728 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 26 × 33 = (4 × 3 )3 = 123 Hence, it’s a perfect cube. (vi) 3087 3087 = 3 × 3 × 7 × 7 × 7 = 32 × 73 Hence, it’s not a perfect cube. |
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