(i) 3375
Step 1: Start making groups of three digits starting from the unit place. i.e.;
3 |
375 |
second |
first |
Group |
Group |
Step 2: First group is 375. Its units digit is 5.
∴ The cube root is also ends with 5.
∴ The units place of the cube root will be 5.
Step 3: Now take the second group,
i.e., 3 we know that 13 < 33 <23
∴ The least number is 1.
∴ The tens digit of a cube root will be 1.
∴ The required number = 15
∴ \(\sqrt[3]{3375}\) = \(\sqrt[3]{15\,\times\,15\,\times15}\) = \(\sqrt[3]{15}{^3}\) = 15
(ii) 5832
Step 1: Start making groups of three digits starting from the unit place.
5 |
832 |
second |
first |
group |
group |
Step 2: The units digit of 832 is 2.
∴ The cube root of the number ends with units digit 8.
[∵ 8 x 8 x 8 = 512]
Step 3: In the second group i.e., 5 lie between 1 and 6
i.e., 13 < 5 < 23
∴ The tens digit of a number will bel.
∴ The required number is 18.
∴ \(\sqrt[3]{5832}\) = \(\sqrt[3]{18\,\times\,18\,\times18}\) = \(\sqrt[3]{18}{^3}\) = 18