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Making use of the cube root table, find the cube root of the following (correct to three decimal places):(i) 1100(ii) 780 (iii) 7800 (iv) 1346 |
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Answer» (i) 1100 = 11×100 ∛1100 = ∛(11×100) = ∛11 × ∛100 By using cube root table, We get, ∛11 = 2.224 ∛100 = 4.6642 ∛1100 = ∛11 × ∛100 = 2.224 × 4.642 = 10.323 ∴ the answer is 10.323 (ii) 780 780 = 78×10 By using cube root table 780 would be in column ∛10x against 78. We get, ∛780 = 9.205 (iii) 7800 7800 = 78×100 ∛7800 = ∛(78×100) = ∛78 × ∛100 By using cube root table, We get, ∛78 = 4.273 ∛100 = 4.6642 ∛7800 = ∛78 × ∛100 = 4.273 × 4.642 = 19.835 ∴ the answer is 19.835 (iv) 1346 1346 = 2×673 ∛1346 = ∛(2×676) = ∛2 × ∛673 Since, 670<673<680 = ∛670 < ∛673 < ∛680 By using cube root table, ∛670 = 8.750 ∛680 = 8.794 For the difference (680-670) which is 10. So the difference in the values = 8.794 – 8.750 = 0.044 For the difference (673-670) which is 3. So the difference in the values = (0.044/10) × 3 = 0.0132 ∛673 = 8.750 + 0.013 = 8.763 ∛1346 = ∛2 × ∛673 = 1.260 × 8.763 = 11.041 ∴ the answer is 11.041 |
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