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Which of the following are perfect cubes?i) 64 (ii) 216 (iii) 243 (iv) 1000 (v) 1728 (vi) 3087 (vii) 4608 (viii) 106480 (ix) 166375 (x) 456533 |
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Answer» (i) 64 Making factors of 64 = 2 × 2 × 2 × 2 × 2 × 2 = 26 = (22)3 = 43 Hence, it’s a perfect cube. (ii) 216 Factors of 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33 = 63 Hence, it’s a perfect cube. (iv) 1000 Factors of 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 23 × 53 = 103 Hence, it’s a perfect cube. (v) 1728 Factors of 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 26 × 33 = (4 × 3 )3 = 123 Hence, it’s a perfect cube. (vi) 3087 Factors of 3087 = 3 × 3 × 7 × 7 × 7 = 32 × 73 Hence, it’s not a perfect cube. (vii) 4608 Factors of 4608 = 2 × 2 × 3 × 113 Hence, it’s not a perfect cube. (viii) 106480 Factors of 106480 = 2 × 2 × 2 × 2 × 5 × 11 × 11 × 11 Hence, it’s not a perfect cube. (ix) 166375 Factors of 166375 = 5 × 5 × 5 × 11 × 11 × 11 = 53 × 113 = 553 Hence, it’s a perfect cube. (x) 456533 Factors of 456533 = 11 × 11 × 11 × 7 × 7 × 7 = 113 × 73 =773 Hence, it’s a perfect cube. |
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