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.
2 |
197 |
second |
first |
group |
group |
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