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Find the cube roots of the following numbers by successive subtraction of numbers: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397,…. (i) 64 (ii) 512 (iii) 1728 |
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Answer» (i) 64 We have, 64 – 1 = 63 63 – 7 = 56 56 – 19 =37 37 – 37 = 0 ∵ Subtraction is performed 4 times. Hence, cube root of 64 is 4. (ii) 512 We have, 512 – 1 = 511 511 – 7 = 504 504 – 19 = 485 485 – 37 = 448 448 – 61 = 387 387 – 91 = 296 296 – 127 = 169 169 – 169 = 0 ∵ Subtraction is performed 8 times. Hence, cube root of 512 is 8. (iii) 1728 We have, 1728 – 1 = 1727 1727 – 7 = 1720 1720 – 19 = 1701 1701 – 37 = 1664 1664 – 91 = 1512 1512 – 127 = 1385 1385 – 169 = 1216 1216 – 217 = 999 999 – 271 = 728 728 – 331 = 397 397 – 397 = 0 ∵ Subtraction is performed 12 times. Hence, cube root of 1728 is 12. |
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