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Find the cube root of the following numbers through estimation’? (i) 512 (ii) 2197 |
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Answer» i) 512 Step 1: Start making groups of three digits starting from the unit place. i.e., \(\overline{512}\) First group is 512 Step 2: First group i.e. 512 will give us the units digit of the cube root. As 512 ends with 2, then its cube root ends with 8 (2 x 2 x 2) So the units place of the cube root will be 8. Step 3: Now take the second group i.e. 0.Which is 03 < 1 < 23 . So the least number is ‘0′. ∴ Tens digit of a cube root of a number be 0. ∴ \(\sqrt[3]{512}\) = 08 = 8 (ii) 2197 Step 1: Start making groups of three digits starting from the unit place.
Step 2: First group i.e., 197 will give us the units digit of the cube root. As 197 ends with 7, its cube root ends with 3. ‘ [∵ 3 x 3 x 3 = 27] ∴ Its units digit is 7. Step 3: Now take the second group i.e.,2 We know that i3 < 2 < 2 ∴ The least number be 1. ∴ The required number is 13. ∴ \(\sqrt[3]{2197}\) = \(\sqrt[3]{13\,\times\,13\,\times13}\) = \(\sqrt[3]{13}{^3}\) = 13 |
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